# 有限正規子群基礎 · 脈衝 R01

本批已通過 Schema、去重、來源快照與獨立答案重算；仍未標記為人工審定。

本題庫已有對應的中英逐步詳解。原題的 candidate 與英文 ai_candidate 狀態保留；AI 覆核、有限計算與 Lean 形式證明分開標示。

batch-20261015-advance-20261113-r01-finite-normal-subgroup-foundations · 2026-10-15 · 100 題

欄序為來源綁定的呈現補充；原始 JSONL 與數學答案不變。

[欄序與來源綁定資料](https://ocme.evemisslab.com/data/i18n/question-output-protocols.json)



## 1. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-subgroup-qualification；資料={"group_table":[[0,1,2,3],[1,2,3,0],[2,3,0,1],[3,0,1,2]],"identity":0,"subset":[0]}。請依 [subset, contains_identity, product_closed, inverse_closed, subgroup, normal_subgroup, certificate] 欄序回答。

查看答案與解釋([0], 是, 是, 是, 是, 是, subgroup_obligations_precede_normality)

Wave6第七層核對=([0], 是, 是, 是, 是, 是, subgroup_obligations_precede_normality)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0001/)

有限正規子群 · qf-mod44-normal-subgroup-qualification · candidate





## 2. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-subgroup-qualification；資料={"group_table":[[0,1,2,3,4,5],[1,2,3,4,5,0],[2,3,4,5,0,1],[3,4,5,0,1,2],[4,5,0,1,2,3],[5,0,1,2,3,4]],"identity":0,"subset":[0,1,2,3,4,5]}。請依 [subset, contains_identity, product_closed, inverse_closed, subgroup, normal_subgroup, certificate] 欄序回答。

查看答案與解釋([0, 1, 2, 3, 4, 5], 是, 是, 是, 是, 是, subgroup_obligations_precede_normality)

Wave6第七層核對=([0, 1, 2, 3, 4, 5], 是, 是, 是, 是, 是, subgroup_obligations_precede_normality)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0002/)

有限正規子群 · qf-mod44-normal-subgroup-qualification · candidate





## 3. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-subgroup-qualification；資料={"group_table":[[0,1,2,3,4,5,6,7],[1,2,3,4,5,6,7,0],[2,3,4,5,6,7,0,1],[3,4,5,6,7,0,1,2],[4,5,6,7,0,1,2,3],[5,6,7,0,1,2,3,4],[6,7,0,1,2,3,4,5],[7,0,1,2,3,4,5,6]],"identity":0,"subset":[0,2,4,6]}。請依 [subset, contains_identity, product_closed, inverse_closed, subgroup, normal_subgroup, certificate] 欄序回答。

查看答案與解釋([0, 2, 4, 6], 是, 是, 是, 是, 是, subgroup_obligations_precede_normality)

Wave6第七層核對=([0, 2, 4, 6], 是, 是, 是, 是, 是, subgroup_obligations_precede_normality)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0003/)

有限正規子群 · qf-mod44-normal-subgroup-qualification · candidate





## 4. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-subgroup-qualification；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9],[1,2,3,4,5,6,7,8,9,0],[2,3,4,5,6,7,8,9,0,1],[3,4,5,6,7,8,9,0,1,2],[4,5,6,7,8,9,0,1,2,3],[5,6,7,8,9,0,1,2,3,4],[6,7,8,9,0,1,2,3,4,5],[7,8,9,0,1,2,3,4,5,6],[8,9,0,1,2,3,4,5,6,7],[9,0,1,2,3,4,5,6,7,8]],"identity":0,"subset":[0,5]}。請依 [subset, contains_identity, product_closed, inverse_closed, subgroup, normal_subgroup, certificate] 欄序回答。

查看答案與解釋([0, 5], 是, 是, 是, 是, 是, subgroup_obligations_precede_normality)

Wave6第七層核對=([0, 5], 是, 是, 是, 是, 是, subgroup_obligations_precede_normality)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0004/)

有限正規子群 · qf-mod44-normal-subgroup-qualification · candidate





## 5. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-subgroup-qualification；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11],[1,2,3,4,5,6,7,8,9,10,11,0],[2,3,4,5,6,7,8,9,10,11,0,1],[3,4,5,6,7,8,9,10,11,0,1,2],[4,5,6,7,8,9,10,11,0,1,2,3],[5,6,7,8,9,10,11,0,1,2,3,4],[6,7,8,9,10,11,0,1,2,3,4,5],[7,8,9,10,11,0,1,2,3,4,5,6],[8,9,10,11,0,1,2,3,4,5,6,7],[9,10,11,0,1,2,3,4,5,6,7,8],[10,11,0,1,2,3,4,5,6,7,8,9],[11,0,1,2,3,4,5,6,7,8,9,10]],"identity":0,"subset":[0,1]}。請依 [subset, contains_identity, product_closed, inverse_closed, subgroup, normal_subgroup, certificate] 欄序回答。

查看答案與解釋([0, 1], 是, 否, 否, 否, 否, subgroup_obligations_precede_normality)

Wave6第七層核對=([0, 1], 是, 否, 否, 否, 否, subgroup_obligations_precede_normality)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0005/)

有限正規子群 · qf-mod44-normal-subgroup-qualification · candidate





## 6. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-subgroup-qualification；資料={"group_table":[[3,0,1,2],[0,1,2,3],[1,2,3,0],[2,3,0,1]],"identity":1,"subset":[1]}。請依 [subset, contains_identity, product_closed, inverse_closed, subgroup, normal_subgroup, certificate] 欄序回答。

查看答案與解釋([1], 是, 是, 是, 是, 是, subgroup_obligations_precede_normality)

Wave6第七層核對=([1], 是, 是, 是, 是, 是, subgroup_obligations_precede_normality)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0006/)

有限正規子群 · qf-mod44-normal-subgroup-qualification · candidate





## 7. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-subgroup-qualification；資料={"group_table":[[5,0,1,2,3,4],[0,1,2,3,4,5],[1,2,3,4,5,0],[2,3,4,5,0,1],[3,4,5,0,1,2],[4,5,0,1,2,3]],"identity":1,"subset":[0,1,2,3,4,5]}。請依 [subset, contains_identity, product_closed, inverse_closed, subgroup, normal_subgroup, certificate] 欄序回答。

查看答案與解釋([0, 1, 2, 3, 4, 5], 是, 是, 是, 是, 是, subgroup_obligations_precede_normality)

Wave6第七層核對=([0, 1, 2, 3, 4, 5], 是, 是, 是, 是, 是, subgroup_obligations_precede_normality)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0007/)

有限正規子群 · qf-mod44-normal-subgroup-qualification · candidate





## 8. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-subgroup-qualification；資料={"group_table":[[7,0,1,2,3,4,5,6],[0,1,2,3,4,5,6,7],[1,2,3,4,5,6,7,0],[2,3,4,5,6,7,0,1],[3,4,5,6,7,0,1,2],[4,5,6,7,0,1,2,3],[5,6,7,0,1,2,3,4],[6,7,0,1,2,3,4,5]],"identity":1,"subset":[1,3,5,7]}。請依 [subset, contains_identity, product_closed, inverse_closed, subgroup, normal_subgroup, certificate] 欄序回答。

查看答案與解釋([1, 3, 5, 7], 是, 是, 是, 是, 是, subgroup_obligations_precede_normality)

Wave6第七層核對=([1, 3, 5, 7], 是, 是, 是, 是, 是, subgroup_obligations_precede_normality)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0008/)

有限正規子群 · qf-mod44-normal-subgroup-qualification · candidate





## 9. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-subgroup-qualification；資料={"group_table":[[9,0,1,2,3,4,5,6,7,8],[0,1,2,3,4,5,6,7,8,9],[1,2,3,4,5,6,7,8,9,0],[2,3,4,5,6,7,8,9,0,1],[3,4,5,6,7,8,9,0,1,2],[4,5,6,7,8,9,0,1,2,3],[5,6,7,8,9,0,1,2,3,4],[6,7,8,9,0,1,2,3,4,5],[7,8,9,0,1,2,3,4,5,6],[8,9,0,1,2,3,4,5,6,7]],"identity":1,"subset":[1,6]}。請依 [subset, contains_identity, product_closed, inverse_closed, subgroup, normal_subgroup, certificate] 欄序回答。

查看答案與解釋([1, 6], 是, 是, 是, 是, 是, subgroup_obligations_precede_normality)

Wave6第七層核對=([1, 6], 是, 是, 是, 是, 是, subgroup_obligations_precede_normality)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0009/)

有限正規子群 · qf-mod44-normal-subgroup-qualification · candidate





## 10. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-subgroup-qualification；資料={"group_table":[[11,0,1,2,3,4,5,6,7,8,9,10],[0,1,2,3,4,5,6,7,8,9,10,11],[1,2,3,4,5,6,7,8,9,10,11,0],[2,3,4,5,6,7,8,9,10,11,0,1],[3,4,5,6,7,8,9,10,11,0,1,2],[4,5,6,7,8,9,10,11,0,1,2,3],[5,6,7,8,9,10,11,0,1,2,3,4],[6,7,8,9,10,11,0,1,2,3,4,5],[7,8,9,10,11,0,1,2,3,4,5,6],[8,9,10,11,0,1,2,3,4,5,6,7],[9,10,11,0,1,2,3,4,5,6,7,8],[10,11,0,1,2,3,4,5,6,7,8,9]],"identity":1,"subset":[1,2]}。請依 [subset, contains_identity, product_closed, inverse_closed, subgroup, normal_subgroup, certificate] 欄序回答。

查看答案與解釋([1, 2], 是, 否, 否, 否, 否, subgroup_obligations_precede_normality)

Wave6第七層核對=([1, 2], 是, 否, 否, 否, 否, subgroup_obligations_precede_normality)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0010/)

有限正規子群 · qf-mod44-normal-subgroup-qualification · candidate





## 11. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-subgroup-qualification；資料={"group_table":[[2,3,0,1],[3,0,1,2],[0,1,2,3],[1,2,3,0]],"identity":2,"subset":[2]}。請依 [subset, contains_identity, product_closed, inverse_closed, subgroup, normal_subgroup, certificate] 欄序回答。

查看答案與解釋([2], 是, 是, 是, 是, 是, subgroup_obligations_precede_normality)

Wave6第七層核對=([2], 是, 是, 是, 是, 是, subgroup_obligations_precede_normality)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0011/)

有限正規子群 · qf-mod44-normal-subgroup-qualification · candidate





## 12. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-subgroup-qualification；資料={"group_table":[[4,5,0,1,2,3],[5,0,1,2,3,4],[0,1,2,3,4,5],[1,2,3,4,5,0],[2,3,4,5,0,1],[3,4,5,0,1,2]],"identity":2,"subset":[0,1,2,3,4,5]}。請依 [subset, contains_identity, product_closed, inverse_closed, subgroup, normal_subgroup, certificate] 欄序回答。

查看答案與解釋([0, 1, 2, 3, 4, 5], 是, 是, 是, 是, 是, subgroup_obligations_precede_normality)

Wave6第七層核對=([0, 1, 2, 3, 4, 5], 是, 是, 是, 是, 是, subgroup_obligations_precede_normality)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0012/)

有限正規子群 · qf-mod44-normal-subgroup-qualification · candidate





## 13. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-subgroup-qualification；資料={"group_table":[[6,7,0,1,2,3,4,5],[7,0,1,2,3,4,5,6],[0,1,2,3,4,5,6,7],[1,2,3,4,5,6,7,0],[2,3,4,5,6,7,0,1],[3,4,5,6,7,0,1,2],[4,5,6,7,0,1,2,3],[5,6,7,0,1,2,3,4]],"identity":2,"subset":[0,2,4,6]}。請依 [subset, contains_identity, product_closed, inverse_closed, subgroup, normal_subgroup, certificate] 欄序回答。

查看答案與解釋([0, 2, 4, 6], 是, 是, 是, 是, 是, subgroup_obligations_precede_normality)

Wave6第七層核對=([0, 2, 4, 6], 是, 是, 是, 是, 是, subgroup_obligations_precede_normality)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0013/)

有限正規子群 · qf-mod44-normal-subgroup-qualification · candidate





## 14. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-subgroup-qualification；資料={"group_table":[[8,9,0,1,2,3,4,5,6,7],[9,0,1,2,3,4,5,6,7,8],[0,1,2,3,4,5,6,7,8,9],[1,2,3,4,5,6,7,8,9,0],[2,3,4,5,6,7,8,9,0,1],[3,4,5,6,7,8,9,0,1,2],[4,5,6,7,8,9,0,1,2,3],[5,6,7,8,9,0,1,2,3,4],[6,7,8,9,0,1,2,3,4,5],[7,8,9,0,1,2,3,4,5,6]],"identity":2,"subset":[2,7]}。請依 [subset, contains_identity, product_closed, inverse_closed, subgroup, normal_subgroup, certificate] 欄序回答。

查看答案與解釋([2, 7], 是, 是, 是, 是, 是, subgroup_obligations_precede_normality)

Wave6第七層核對=([2, 7], 是, 是, 是, 是, 是, subgroup_obligations_precede_normality)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0014/)

有限正規子群 · qf-mod44-normal-subgroup-qualification · candidate





## 15. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-subgroup-qualification；資料={"group_table":[[10,11,0,1,2,3,4,5,6,7,8,9],[11,0,1,2,3,4,5,6,7,8,9,10],[0,1,2,3,4,5,6,7,8,9,10,11],[1,2,3,4,5,6,7,8,9,10,11,0],[2,3,4,5,6,7,8,9,10,11,0,1],[3,4,5,6,7,8,9,10,11,0,1,2],[4,5,6,7,8,9,10,11,0,1,2,3],[5,6,7,8,9,10,11,0,1,2,3,4],[6,7,8,9,10,11,0,1,2,3,4,5],[7,8,9,10,11,0,1,2,3,4,5,6],[8,9,10,11,0,1,2,3,4,5,6,7],[9,10,11,0,1,2,3,4,5,6,7,8]],"identity":2,"subset":[2,3]}。請依 [subset, contains_identity, product_closed, inverse_closed, subgroup, normal_subgroup, certificate] 欄序回答。

查看答案與解釋([2, 3], 是, 否, 否, 否, 否, subgroup_obligations_precede_normality)

Wave6第七層核對=([2, 3], 是, 否, 否, 否, 否, subgroup_obligations_precede_normality)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0015/)

有限正規子群 · qf-mod44-normal-subgroup-qualification · candidate





## 16. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-subgroup-qualification；資料={"group_table":[[1,2,3,0],[2,3,0,1],[3,0,1,2],[0,1,2,3]],"identity":3,"subset":[3]}。請依 [subset, contains_identity, product_closed, inverse_closed, subgroup, normal_subgroup, certificate] 欄序回答。

查看答案與解釋([3], 是, 是, 是, 是, 是, subgroup_obligations_precede_normality)

Wave6第七層核對=([3], 是, 是, 是, 是, 是, subgroup_obligations_precede_normality)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0016/)

有限正規子群 · qf-mod44-normal-subgroup-qualification · candidate





## 17. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-subgroup-qualification；資料={"group_table":[[3,4,5,0,1,2],[4,5,0,1,2,3],[5,0,1,2,3,4],[0,1,2,3,4,5],[1,2,3,4,5,0],[2,3,4,5,0,1]],"identity":3,"subset":[0,1,2,3,4,5]}。請依 [subset, contains_identity, product_closed, inverse_closed, subgroup, normal_subgroup, certificate] 欄序回答。

查看答案與解釋([0, 1, 2, 3, 4, 5], 是, 是, 是, 是, 是, subgroup_obligations_precede_normality)

Wave6第七層核對=([0, 1, 2, 3, 4, 5], 是, 是, 是, 是, 是, subgroup_obligations_precede_normality)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0017/)

有限正規子群 · qf-mod44-normal-subgroup-qualification · candidate





## 18. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-subgroup-qualification；資料={"group_table":[[5,6,7,0,1,2,3,4],[6,7,0,1,2,3,4,5],[7,0,1,2,3,4,5,6],[0,1,2,3,4,5,6,7],[1,2,3,4,5,6,7,0],[2,3,4,5,6,7,0,1],[3,4,5,6,7,0,1,2],[4,5,6,7,0,1,2,3]],"identity":3,"subset":[1,3,5,7]}。請依 [subset, contains_identity, product_closed, inverse_closed, subgroup, normal_subgroup, certificate] 欄序回答。

查看答案與解釋([1, 3, 5, 7], 是, 是, 是, 是, 是, subgroup_obligations_precede_normality)

Wave6第七層核對=([1, 3, 5, 7], 是, 是, 是, 是, 是, subgroup_obligations_precede_normality)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0018/)

有限正規子群 · qf-mod44-normal-subgroup-qualification · candidate





## 19. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-subgroup-qualification；資料={"group_table":[[7,8,9,0,1,2,3,4,5,6],[8,9,0,1,2,3,4,5,6,7],[9,0,1,2,3,4,5,6,7,8],[0,1,2,3,4,5,6,7,8,9],[1,2,3,4,5,6,7,8,9,0],[2,3,4,5,6,7,8,9,0,1],[3,4,5,6,7,8,9,0,1,2],[4,5,6,7,8,9,0,1,2,3],[5,6,7,8,9,0,1,2,3,4],[6,7,8,9,0,1,2,3,4,5]],"identity":3,"subset":[3,8]}。請依 [subset, contains_identity, product_closed, inverse_closed, subgroup, normal_subgroup, certificate] 欄序回答。

查看答案與解釋([3, 8], 是, 是, 是, 是, 是, subgroup_obligations_precede_normality)

Wave6第七層核對=([3, 8], 是, 是, 是, 是, 是, subgroup_obligations_precede_normality)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0019/)

有限正規子群 · qf-mod44-normal-subgroup-qualification · candidate





## 20. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-subgroup-qualification；資料={"group_table":[[9,10,11,0,1,2,3,4,5,6,7,8],[10,11,0,1,2,3,4,5,6,7,8,9],[11,0,1,2,3,4,5,6,7,8,9,10],[0,1,2,3,4,5,6,7,8,9,10,11],[1,2,3,4,5,6,7,8,9,10,11,0],[2,3,4,5,6,7,8,9,10,11,0,1],[3,4,5,6,7,8,9,10,11,0,1,2],[4,5,6,7,8,9,10,11,0,1,2,3],[5,6,7,8,9,10,11,0,1,2,3,4],[6,7,8,9,10,11,0,1,2,3,4,5],[7,8,9,10,11,0,1,2,3,4,5,6],[8,9,10,11,0,1,2,3,4,5,6,7]],"identity":3,"subset":[3,4]}。請依 [subset, contains_identity, product_closed, inverse_closed, subgroup, normal_subgroup, certificate] 欄序回答。

查看答案與解釋([3, 4], 是, 否, 否, 否, 否, subgroup_obligations_precede_normality)

Wave6第七層核對=([3, 4], 是, 否, 否, 否, 否, subgroup_obligations_precede_normality)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0020/)

有限正規子群 · qf-mod44-normal-subgroup-qualification · candidate





## 21. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-subgroup-qualification；資料={"group_table":[[0,1,2,3],[1,0,3,2],[2,3,1,0],[3,2,0,1]],"identity":0,"subset":[0]}。請依 [subset, contains_identity, product_closed, inverse_closed, subgroup, normal_subgroup, certificate] 欄序回答。

查看答案與解釋([0], 是, 是, 是, 是, 是, subgroup_obligations_precede_normality)

Wave6第七層核對=([0], 是, 是, 是, 是, 是, subgroup_obligations_precede_normality)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0021/)

有限正規子群 · qf-mod44-normal-subgroup-qualification · candidate





## 22. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-subgroup-qualification；資料={"group_table":[[2,3,4,5,0,1],[3,4,5,0,1,2],[4,5,0,1,2,3],[5,0,1,2,3,4],[0,1,2,3,4,5],[1,2,3,4,5,0]],"identity":4,"subset":[0,1,2,3,4,5]}。請依 [subset, contains_identity, product_closed, inverse_closed, subgroup, normal_subgroup, certificate] 欄序回答。

查看答案與解釋([0, 1, 2, 3, 4, 5], 是, 是, 是, 是, 是, subgroup_obligations_precede_normality)

Wave6第七層核對=([0, 1, 2, 3, 4, 5], 是, 是, 是, 是, 是, subgroup_obligations_precede_normality)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0022/)

有限正規子群 · qf-mod44-normal-subgroup-qualification · candidate





## 23. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-subgroup-qualification；資料={"group_table":[[4,5,6,7,0,1,2,3],[5,6,7,0,1,2,3,4],[6,7,0,1,2,3,4,5],[7,0,1,2,3,4,5,6],[0,1,2,3,4,5,6,7],[1,2,3,4,5,6,7,0],[2,3,4,5,6,7,0,1],[3,4,5,6,7,0,1,2]],"identity":4,"subset":[0,2,4,6]}。請依 [subset, contains_identity, product_closed, inverse_closed, subgroup, normal_subgroup, certificate] 欄序回答。

查看答案與解釋([0, 2, 4, 6], 是, 是, 是, 是, 是, subgroup_obligations_precede_normality)

Wave6第七層核對=([0, 2, 4, 6], 是, 是, 是, 是, 是, subgroup_obligations_precede_normality)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0023/)

有限正規子群 · qf-mod44-normal-subgroup-qualification · candidate





## 24. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-subgroup-qualification；資料={"group_table":[[6,7,8,9,0,1,2,3,4,5],[7,8,9,0,1,2,3,4,5,6],[8,9,0,1,2,3,4,5,6,7],[9,0,1,2,3,4,5,6,7,8],[0,1,2,3,4,5,6,7,8,9],[1,2,3,4,5,6,7,8,9,0],[2,3,4,5,6,7,8,9,0,1],[3,4,5,6,7,8,9,0,1,2],[4,5,6,7,8,9,0,1,2,3],[5,6,7,8,9,0,1,2,3,4]],"identity":4,"subset":[4,9]}。請依 [subset, contains_identity, product_closed, inverse_closed, subgroup, normal_subgroup, certificate] 欄序回答。

查看答案與解釋([4, 9], 是, 是, 是, 是, 是, subgroup_obligations_precede_normality)

Wave6第七層核對=([4, 9], 是, 是, 是, 是, 是, subgroup_obligations_precede_normality)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0024/)

有限正規子群 · qf-mod44-normal-subgroup-qualification · candidate





## 25. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-subgroup-qualification；資料={"group_table":[[8,9,10,11,0,1,2,3,4,5,6,7],[9,10,11,0,1,2,3,4,5,6,7,8],[10,11,0,1,2,3,4,5,6,7,8,9],[11,0,1,2,3,4,5,6,7,8,9,10],[0,1,2,3,4,5,6,7,8,9,10,11],[1,2,3,4,5,6,7,8,9,10,11,0],[2,3,4,5,6,7,8,9,10,11,0,1],[3,4,5,6,7,8,9,10,11,0,1,2],[4,5,6,7,8,9,10,11,0,1,2,3],[5,6,7,8,9,10,11,0,1,2,3,4],[6,7,8,9,10,11,0,1,2,3,4,5],[7,8,9,10,11,0,1,2,3,4,5,6]],"identity":4,"subset":[4,5]}。請依 [subset, contains_identity, product_closed, inverse_closed, subgroup, normal_subgroup, certificate] 欄序回答。

查看答案與解釋([4, 5], 是, 否, 否, 否, 否, subgroup_obligations_precede_normality)

Wave6第七層核對=([4, 5], 是, 否, 否, 否, 否, subgroup_obligations_precede_normality)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0025/)

有限正規子群 · qf-mod44-normal-subgroup-qualification · candidate





## 26. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-conjugate-set-audit；資料={"group_table":[[0,1,2,3],[1,2,3,0],[2,3,0,1],[3,0,1,2]],"identity":0,"subset":[0]}。請依 [subgroup, conjugate_rows, normal, certificate] 欄序回答。

查看答案與解釋([0], [[0, [0], 是], [1, [0], 是], [2, [0], 是], [3, [0], 是]], 是, every_group_element_conjugates_H_to_itself)

Wave6第七層核對=([0], [[0, [0], 是], [1, [0], 是], [2, [0], 是], [3, [0], 是]], 是, every_group_element_conjugates_H_to_itself)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0026/)

有限正規子群 · qf-mod44-normal-conjugate-set-audit · candidate





## 27. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-conjugate-set-audit；資料={"group_table":[[0,1,2,3,4,5],[1,2,3,4,5,0],[2,3,4,5,0,1],[3,4,5,0,1,2],[4,5,0,1,2,3],[5,0,1,2,3,4]],"identity":0,"subset":[0,1,2,3,4,5]}。請依 [subgroup, conjugate_rows, normal, certificate] 欄序回答。

查看答案與解釋([0, 1, 2, 3, 4, 5], [[0, [0, 1, 2, 3, 4, 5], 是], [1, [0, 1, 2, 3, 4, 5], 是], [2, [0, 1, 2, 3, 4, 5], 是], [3, [0, 1, 2, 3, 4, 5], 是], [4, [0, 1, 2, 3, 4, 5], 是], [5, [0, 1, 2, 3, 4, 5], 是]], 是, every_group_element_conjugates_H_to_itself)

Wave6第七層核對=([0, 1, 2, 3, 4, 5], [[0, [0, 1, 2, 3, 4, 5], 是], [1, [0, 1, 2, 3, 4, 5], 是], [2, [0, 1, 2, 3, 4, 5], 是], [3, [0, 1, 2, 3, 4, 5], 是], [4, [0, 1, 2, 3, 4, 5], 是], [5, [0, 1, 2, 3, 4, 5], 是]], 是, every_group_element_conjugates_H_to_itself)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0027/)

有限正規子群 · qf-mod44-normal-conjugate-set-audit · candidate





## 28. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-conjugate-set-audit；資料={"group_table":[[0,1,2,3,4,5,6,7],[1,2,3,4,5,6,7,0],[2,3,4,5,6,7,0,1],[3,4,5,6,7,0,1,2],[4,5,6,7,0,1,2,3],[5,6,7,0,1,2,3,4],[6,7,0,1,2,3,4,5],[7,0,1,2,3,4,5,6]],"identity":0,"subset":[0]}。請依 [subgroup, conjugate_rows, normal, certificate] 欄序回答。

查看答案與解釋([0], [[0, [0], 是], [1, [0], 是], [2, [0], 是], [3, [0], 是], [4, [0], 是], [5, [0], 是], [6, [0], 是], [7, [0], 是]], 是, every_group_element_conjugates_H_to_itself)

Wave6第七層核對=([0], [[0, [0], 是], [1, [0], 是], [2, [0], 是], [3, [0], 是], [4, [0], 是], [5, [0], 是], [6, [0], 是], [7, [0], 是]], 是, every_group_element_conjugates_H_to_itself)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0028/)

有限正規子群 · qf-mod44-normal-conjugate-set-audit · candidate





## 29. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-conjugate-set-audit；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9],[1,2,3,4,5,6,7,8,9,0],[2,3,4,5,6,7,8,9,0,1],[3,4,5,6,7,8,9,0,1,2],[4,5,6,7,8,9,0,1,2,3],[5,6,7,8,9,0,1,2,3,4],[6,7,8,9,0,1,2,3,4,5],[7,8,9,0,1,2,3,4,5,6],[8,9,0,1,2,3,4,5,6,7],[9,0,1,2,3,4,5,6,7,8]],"identity":0,"subset":[0,1,2,3,4,5,6,7,8,9]}。請依 [subgroup, conjugate_rows, normal, certificate] 欄序回答。

查看答案與解釋([0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [[0, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [1, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [2, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [3, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [4, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [5, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [6, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [7, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [8, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [9, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是]], 是, every_group_element_conjugates_H_to_itself)

Wave6第七層核對=([0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [[0, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [1, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [2, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [3, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [4, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [5, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [6, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [7, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [8, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [9, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是]], 是, every_group_element_conjugates_H_to_itself)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0029/)

有限正規子群 · qf-mod44-normal-conjugate-set-audit · candidate





## 30. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-conjugate-set-audit；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11],[1,2,3,4,5,6,7,8,9,10,11,0],[2,3,4,5,6,7,8,9,10,11,0,1],[3,4,5,6,7,8,9,10,11,0,1,2],[4,5,6,7,8,9,10,11,0,1,2,3],[5,6,7,8,9,10,11,0,1,2,3,4],[6,7,8,9,10,11,0,1,2,3,4,5],[7,8,9,10,11,0,1,2,3,4,5,6],[8,9,10,11,0,1,2,3,4,5,6,7],[9,10,11,0,1,2,3,4,5,6,7,8],[10,11,0,1,2,3,4,5,6,7,8,9],[11,0,1,2,3,4,5,6,7,8,9,10]],"identity":0,"subset":[0]}。請依 [subgroup, conjugate_rows, normal, certificate] 欄序回答。

查看答案與解釋([0], [[0, [0], 是], [1, [0], 是], [2, [0], 是], [3, [0], 是], [4, [0], 是], [5, [0], 是], [6, [0], 是], [7, [0], 是], [8, [0], 是], [9, [0], 是], [10, [0], 是], [11, [0], 是]], 是, every_group_element_conjugates_H_to_itself)

Wave6第七層核對=([0], [[0, [0], 是], [1, [0], 是], [2, [0], 是], [3, [0], 是], [4, [0], 是], [5, [0], 是], [6, [0], 是], [7, [0], 是], [8, [0], 是], [9, [0], 是], [10, [0], 是], [11, [0], 是]], 是, every_group_element_conjugates_H_to_itself)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0030/)

有限正規子群 · qf-mod44-normal-conjugate-set-audit · candidate





## 31. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-conjugate-set-audit；資料={"group_table":[[3,0,1,2],[0,1,2,3],[1,2,3,0],[2,3,0,1]],"identity":1,"subset":[0,1,2,3]}。請依 [subgroup, conjugate_rows, normal, certificate] 欄序回答。

查看答案與解釋([0, 1, 2, 3], [[0, [0, 1, 2, 3], 是], [1, [0, 1, 2, 3], 是], [2, [0, 1, 2, 3], 是], [3, [0, 1, 2, 3], 是]], 是, every_group_element_conjugates_H_to_itself)

Wave6第七層核對=([0, 1, 2, 3], [[0, [0, 1, 2, 3], 是], [1, [0, 1, 2, 3], 是], [2, [0, 1, 2, 3], 是], [3, [0, 1, 2, 3], 是]], 是, every_group_element_conjugates_H_to_itself)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0031/)

有限正規子群 · qf-mod44-normal-conjugate-set-audit · candidate





## 32. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-conjugate-set-audit；資料={"group_table":[[5,0,1,2,3,4],[0,1,2,3,4,5],[1,2,3,4,5,0],[2,3,4,5,0,1],[3,4,5,0,1,2],[4,5,0,1,2,3]],"identity":1,"subset":[1]}。請依 [subgroup, conjugate_rows, normal, certificate] 欄序回答。

查看答案與解釋([1], [[0, [1], 是], [1, [1], 是], [2, [1], 是], [3, [1], 是], [4, [1], 是], [5, [1], 是]], 是, every_group_element_conjugates_H_to_itself)

Wave6第七層核對=([1], [[0, [1], 是], [1, [1], 是], [2, [1], 是], [3, [1], 是], [4, [1], 是], [5, [1], 是]], 是, every_group_element_conjugates_H_to_itself)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0032/)

有限正規子群 · qf-mod44-normal-conjugate-set-audit · candidate





## 33. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-conjugate-set-audit；資料={"group_table":[[7,0,1,2,3,4,5,6],[0,1,2,3,4,5,6,7],[1,2,3,4,5,6,7,0],[2,3,4,5,6,7,0,1],[3,4,5,6,7,0,1,2],[4,5,6,7,0,1,2,3],[5,6,7,0,1,2,3,4],[6,7,0,1,2,3,4,5]],"identity":1,"subset":[0,1,2,3,4,5,6,7]}。請依 [subgroup, conjugate_rows, normal, certificate] 欄序回答。

查看答案與解釋([0, 1, 2, 3, 4, 5, 6, 7], [[0, [0, 1, 2, 3, 4, 5, 6, 7], 是], [1, [0, 1, 2, 3, 4, 5, 6, 7], 是], [2, [0, 1, 2, 3, 4, 5, 6, 7], 是], [3, [0, 1, 2, 3, 4, 5, 6, 7], 是], [4, [0, 1, 2, 3, 4, 5, 6, 7], 是], [5, [0, 1, 2, 3, 4, 5, 6, 7], 是], [6, [0, 1, 2, 3, 4, 5, 6, 7], 是], [7, [0, 1, 2, 3, 4, 5, 6, 7], 是]], 是, every_group_element_conjugates_H_to_itself)

Wave6第七層核對=([0, 1, 2, 3, 4, 5, 6, 7], [[0, [0, 1, 2, 3, 4, 5, 6, 7], 是], [1, [0, 1, 2, 3, 4, 5, 6, 7], 是], [2, [0, 1, 2, 3, 4, 5, 6, 7], 是], [3, [0, 1, 2, 3, 4, 5, 6, 7], 是], [4, [0, 1, 2, 3, 4, 5, 6, 7], 是], [5, [0, 1, 2, 3, 4, 5, 6, 7], 是], [6, [0, 1, 2, 3, 4, 5, 6, 7], 是], [7, [0, 1, 2, 3, 4, 5, 6, 7], 是]], 是, every_group_element_conjugates_H_to_itself)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0033/)

有限正規子群 · qf-mod44-normal-conjugate-set-audit · candidate





## 34. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-conjugate-set-audit；資料={"group_table":[[9,0,1,2,3,4,5,6,7,8],[0,1,2,3,4,5,6,7,8,9],[1,2,3,4,5,6,7,8,9,0],[2,3,4,5,6,7,8,9,0,1],[3,4,5,6,7,8,9,0,1,2],[4,5,6,7,8,9,0,1,2,3],[5,6,7,8,9,0,1,2,3,4],[6,7,8,9,0,1,2,3,4,5],[7,8,9,0,1,2,3,4,5,6],[8,9,0,1,2,3,4,5,6,7]],"identity":1,"subset":[1]}。請依 [subgroup, conjugate_rows, normal, certificate] 欄序回答。

查看答案與解釋([1], [[0, [1], 是], [1, [1], 是], [2, [1], 是], [3, [1], 是], [4, [1], 是], [5, [1], 是], [6, [1], 是], [7, [1], 是], [8, [1], 是], [9, [1], 是]], 是, every_group_element_conjugates_H_to_itself)

Wave6第七層核對=([1], [[0, [1], 是], [1, [1], 是], [2, [1], 是], [3, [1], 是], [4, [1], 是], [5, [1], 是], [6, [1], 是], [7, [1], 是], [8, [1], 是], [9, [1], 是]], 是, every_group_element_conjugates_H_to_itself)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0034/)

有限正規子群 · qf-mod44-normal-conjugate-set-audit · candidate





## 35. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-conjugate-set-audit；資料={"group_table":[[11,0,1,2,3,4,5,6,7,8,9,10],[0,1,2,3,4,5,6,7,8,9,10,11],[1,2,3,4,5,6,7,8,9,10,11,0],[2,3,4,5,6,7,8,9,10,11,0,1],[3,4,5,6,7,8,9,10,11,0,1,2],[4,5,6,7,8,9,10,11,0,1,2,3],[5,6,7,8,9,10,11,0,1,2,3,4],[6,7,8,9,10,11,0,1,2,3,4,5],[7,8,9,10,11,0,1,2,3,4,5,6],[8,9,10,11,0,1,2,3,4,5,6,7],[9,10,11,0,1,2,3,4,5,6,7,8],[10,11,0,1,2,3,4,5,6,7,8,9]],"identity":1,"subset":[0,1,2,3,4,5,6,7,8,9,10,11]}。請依 [subgroup, conjugate_rows, normal, certificate] 欄序回答。

查看答案與解釋([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [[0, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [1, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [2, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [3, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [4, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [5, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [6, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [7, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [8, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [9, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [10, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [11, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是]], 是, every_group_element_conjugates_H_to_itself)

Wave6第七層核對=([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [[0, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [1, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [2, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [3, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [4, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [5, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [6, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [7, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [8, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [9, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [10, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [11, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是]], 是, every_group_element_conjugates_H_to_itself)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0035/)

有限正規子群 · qf-mod44-normal-conjugate-set-audit · candidate





## 36. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-conjugate-set-audit；資料={"group_table":[[2,3,0,1],[3,0,1,2],[0,1,2,3],[1,2,3,0]],"identity":2,"subset":[2]}。請依 [subgroup, conjugate_rows, normal, certificate] 欄序回答。

查看答案與解釋([2], [[0, [2], 是], [1, [2], 是], [2, [2], 是], [3, [2], 是]], 是, every_group_element_conjugates_H_to_itself)

Wave6第七層核對=([2], [[0, [2], 是], [1, [2], 是], [2, [2], 是], [3, [2], 是]], 是, every_group_element_conjugates_H_to_itself)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0036/)

有限正規子群 · qf-mod44-normal-conjugate-set-audit · candidate





## 37. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-conjugate-set-audit；資料={"group_table":[[4,5,0,1,2,3],[5,0,1,2,3,4],[0,1,2,3,4,5],[1,2,3,4,5,0],[2,3,4,5,0,1],[3,4,5,0,1,2]],"identity":2,"subset":[0,1,2,3,4,5]}。請依 [subgroup, conjugate_rows, normal, certificate] 欄序回答。

查看答案與解釋([0, 1, 2, 3, 4, 5], [[0, [0, 1, 2, 3, 4, 5], 是], [1, [0, 1, 2, 3, 4, 5], 是], [2, [0, 1, 2, 3, 4, 5], 是], [3, [0, 1, 2, 3, 4, 5], 是], [4, [0, 1, 2, 3, 4, 5], 是], [5, [0, 1, 2, 3, 4, 5], 是]], 是, every_group_element_conjugates_H_to_itself)

Wave6第七層核對=([0, 1, 2, 3, 4, 5], [[0, [0, 1, 2, 3, 4, 5], 是], [1, [0, 1, 2, 3, 4, 5], 是], [2, [0, 1, 2, 3, 4, 5], 是], [3, [0, 1, 2, 3, 4, 5], 是], [4, [0, 1, 2, 3, 4, 5], 是], [5, [0, 1, 2, 3, 4, 5], 是]], 是, every_group_element_conjugates_H_to_itself)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0037/)

有限正規子群 · qf-mod44-normal-conjugate-set-audit · candidate





## 38. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-conjugate-set-audit；資料={"group_table":[[6,7,0,1,2,3,4,5],[7,0,1,2,3,4,5,6],[0,1,2,3,4,5,6,7],[1,2,3,4,5,6,7,0],[2,3,4,5,6,7,0,1],[3,4,5,6,7,0,1,2],[4,5,6,7,0,1,2,3],[5,6,7,0,1,2,3,4]],"identity":2,"subset":[2]}。請依 [subgroup, conjugate_rows, normal, certificate] 欄序回答。

查看答案與解釋([2], [[0, [2], 是], [1, [2], 是], [2, [2], 是], [3, [2], 是], [4, [2], 是], [5, [2], 是], [6, [2], 是], [7, [2], 是]], 是, every_group_element_conjugates_H_to_itself)

Wave6第七層核對=([2], [[0, [2], 是], [1, [2], 是], [2, [2], 是], [3, [2], 是], [4, [2], 是], [5, [2], 是], [6, [2], 是], [7, [2], 是]], 是, every_group_element_conjugates_H_to_itself)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0038/)

有限正規子群 · qf-mod44-normal-conjugate-set-audit · candidate





## 39. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-conjugate-set-audit；資料={"group_table":[[8,9,0,1,2,3,4,5,6,7],[9,0,1,2,3,4,5,6,7,8],[0,1,2,3,4,5,6,7,8,9],[1,2,3,4,5,6,7,8,9,0],[2,3,4,5,6,7,8,9,0,1],[3,4,5,6,7,8,9,0,1,2],[4,5,6,7,8,9,0,1,2,3],[5,6,7,8,9,0,1,2,3,4],[6,7,8,9,0,1,2,3,4,5],[7,8,9,0,1,2,3,4,5,6]],"identity":2,"subset":[0,1,2,3,4,5,6,7,8,9]}。請依 [subgroup, conjugate_rows, normal, certificate] 欄序回答。

查看答案與解釋([0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [[0, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [1, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [2, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [3, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [4, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [5, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [6, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [7, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [8, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [9, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是]], 是, every_group_element_conjugates_H_to_itself)

Wave6第七層核對=([0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [[0, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [1, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [2, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [3, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [4, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [5, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [6, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [7, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [8, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [9, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是]], 是, every_group_element_conjugates_H_to_itself)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0039/)

有限正規子群 · qf-mod44-normal-conjugate-set-audit · candidate





## 40. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-conjugate-set-audit；資料={"group_table":[[10,11,0,1,2,3,4,5,6,7,8,9],[11,0,1,2,3,4,5,6,7,8,9,10],[0,1,2,3,4,5,6,7,8,9,10,11],[1,2,3,4,5,6,7,8,9,10,11,0],[2,3,4,5,6,7,8,9,10,11,0,1],[3,4,5,6,7,8,9,10,11,0,1,2],[4,5,6,7,8,9,10,11,0,1,2,3],[5,6,7,8,9,10,11,0,1,2,3,4],[6,7,8,9,10,11,0,1,2,3,4,5],[7,8,9,10,11,0,1,2,3,4,5,6],[8,9,10,11,0,1,2,3,4,5,6,7],[9,10,11,0,1,2,3,4,5,6,7,8]],"identity":2,"subset":[2]}。請依 [subgroup, conjugate_rows, normal, certificate] 欄序回答。

查看答案與解釋([2], [[0, [2], 是], [1, [2], 是], [2, [2], 是], [3, [2], 是], [4, [2], 是], [5, [2], 是], [6, [2], 是], [7, [2], 是], [8, [2], 是], [9, [2], 是], [10, [2], 是], [11, [2], 是]], 是, every_group_element_conjugates_H_to_itself)

Wave6第七層核對=([2], [[0, [2], 是], [1, [2], 是], [2, [2], 是], [3, [2], 是], [4, [2], 是], [5, [2], 是], [6, [2], 是], [7, [2], 是], [8, [2], 是], [9, [2], 是], [10, [2], 是], [11, [2], 是]], 是, every_group_element_conjugates_H_to_itself)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0040/)

有限正規子群 · qf-mod44-normal-conjugate-set-audit · candidate





## 41. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-conjugate-set-audit；資料={"group_table":[[1,2,3,0],[2,3,0,1],[3,0,1,2],[0,1,2,3]],"identity":3,"subset":[0,1,2,3]}。請依 [subgroup, conjugate_rows, normal, certificate] 欄序回答。

查看答案與解釋([0, 1, 2, 3], [[0, [0, 1, 2, 3], 是], [1, [0, 1, 2, 3], 是], [2, [0, 1, 2, 3], 是], [3, [0, 1, 2, 3], 是]], 是, every_group_element_conjugates_H_to_itself)

Wave6第七層核對=([0, 1, 2, 3], [[0, [0, 1, 2, 3], 是], [1, [0, 1, 2, 3], 是], [2, [0, 1, 2, 3], 是], [3, [0, 1, 2, 3], 是]], 是, every_group_element_conjugates_H_to_itself)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0041/)

有限正規子群 · qf-mod44-normal-conjugate-set-audit · candidate





## 42. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-conjugate-set-audit；資料={"group_table":[[3,4,5,0,1,2],[4,5,0,1,2,3],[5,0,1,2,3,4],[0,1,2,3,4,5],[1,2,3,4,5,0],[2,3,4,5,0,1]],"identity":3,"subset":[3]}。請依 [subgroup, conjugate_rows, normal, certificate] 欄序回答。

查看答案與解釋([3], [[0, [3], 是], [1, [3], 是], [2, [3], 是], [3, [3], 是], [4, [3], 是], [5, [3], 是]], 是, every_group_element_conjugates_H_to_itself)

Wave6第七層核對=([3], [[0, [3], 是], [1, [3], 是], [2, [3], 是], [3, [3], 是], [4, [3], 是], [5, [3], 是]], 是, every_group_element_conjugates_H_to_itself)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0042/)

有限正規子群 · qf-mod44-normal-conjugate-set-audit · candidate





## 43. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-conjugate-set-audit；資料={"group_table":[[5,6,7,0,1,2,3,4],[6,7,0,1,2,3,4,5],[7,0,1,2,3,4,5,6],[0,1,2,3,4,5,6,7],[1,2,3,4,5,6,7,0],[2,3,4,5,6,7,0,1],[3,4,5,6,7,0,1,2],[4,5,6,7,0,1,2,3]],"identity":3,"subset":[0,1,2,3,4,5,6,7]}。請依 [subgroup, conjugate_rows, normal, certificate] 欄序回答。

查看答案與解釋([0, 1, 2, 3, 4, 5, 6, 7], [[0, [0, 1, 2, 3, 4, 5, 6, 7], 是], [1, [0, 1, 2, 3, 4, 5, 6, 7], 是], [2, [0, 1, 2, 3, 4, 5, 6, 7], 是], [3, [0, 1, 2, 3, 4, 5, 6, 7], 是], [4, [0, 1, 2, 3, 4, 5, 6, 7], 是], [5, [0, 1, 2, 3, 4, 5, 6, 7], 是], [6, [0, 1, 2, 3, 4, 5, 6, 7], 是], [7, [0, 1, 2, 3, 4, 5, 6, 7], 是]], 是, every_group_element_conjugates_H_to_itself)

Wave6第七層核對=([0, 1, 2, 3, 4, 5, 6, 7], [[0, [0, 1, 2, 3, 4, 5, 6, 7], 是], [1, [0, 1, 2, 3, 4, 5, 6, 7], 是], [2, [0, 1, 2, 3, 4, 5, 6, 7], 是], [3, [0, 1, 2, 3, 4, 5, 6, 7], 是], [4, [0, 1, 2, 3, 4, 5, 6, 7], 是], [5, [0, 1, 2, 3, 4, 5, 6, 7], 是], [6, [0, 1, 2, 3, 4, 5, 6, 7], 是], [7, [0, 1, 2, 3, 4, 5, 6, 7], 是]], 是, every_group_element_conjugates_H_to_itself)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0043/)

有限正規子群 · qf-mod44-normal-conjugate-set-audit · candidate





## 44. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-conjugate-set-audit；資料={"group_table":[[7,8,9,0,1,2,3,4,5,6],[8,9,0,1,2,3,4,5,6,7],[9,0,1,2,3,4,5,6,7,8],[0,1,2,3,4,5,6,7,8,9],[1,2,3,4,5,6,7,8,9,0],[2,3,4,5,6,7,8,9,0,1],[3,4,5,6,7,8,9,0,1,2],[4,5,6,7,8,9,0,1,2,3],[5,6,7,8,9,0,1,2,3,4],[6,7,8,9,0,1,2,3,4,5]],"identity":3,"subset":[3]}。請依 [subgroup, conjugate_rows, normal, certificate] 欄序回答。

查看答案與解釋([3], [[0, [3], 是], [1, [3], 是], [2, [3], 是], [3, [3], 是], [4, [3], 是], [5, [3], 是], [6, [3], 是], [7, [3], 是], [8, [3], 是], [9, [3], 是]], 是, every_group_element_conjugates_H_to_itself)

Wave6第七層核對=([3], [[0, [3], 是], [1, [3], 是], [2, [3], 是], [3, [3], 是], [4, [3], 是], [5, [3], 是], [6, [3], 是], [7, [3], 是], [8, [3], 是], [9, [3], 是]], 是, every_group_element_conjugates_H_to_itself)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0044/)

有限正規子群 · qf-mod44-normal-conjugate-set-audit · candidate





## 45. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-conjugate-set-audit；資料={"group_table":[[9,10,11,0,1,2,3,4,5,6,7,8],[10,11,0,1,2,3,4,5,6,7,8,9],[11,0,1,2,3,4,5,6,7,8,9,10],[0,1,2,3,4,5,6,7,8,9,10,11],[1,2,3,4,5,6,7,8,9,10,11,0],[2,3,4,5,6,7,8,9,10,11,0,1],[3,4,5,6,7,8,9,10,11,0,1,2],[4,5,6,7,8,9,10,11,0,1,2,3],[5,6,7,8,9,10,11,0,1,2,3,4],[6,7,8,9,10,11,0,1,2,3,4,5],[7,8,9,10,11,0,1,2,3,4,5,6],[8,9,10,11,0,1,2,3,4,5,6,7]],"identity":3,"subset":[0,1,2,3,4,5,6,7,8,9,10,11]}。請依 [subgroup, conjugate_rows, normal, certificate] 欄序回答。

查看答案與解釋([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [[0, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [1, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [2, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [3, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [4, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [5, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [6, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [7, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [8, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [9, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [10, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [11, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是]], 是, every_group_element_conjugates_H_to_itself)

Wave6第七層核對=([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [[0, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [1, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [2, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [3, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [4, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [5, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [6, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [7, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [8, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [9, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [10, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [11, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是]], 是, every_group_element_conjugates_H_to_itself)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0045/)

有限正規子群 · qf-mod44-normal-conjugate-set-audit · candidate





## 46. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-conjugate-set-audit；資料={"group_table":[[0,1,2,3],[1,0,3,2],[2,3,1,0],[3,2,0,1]],"identity":0,"subset":[0]}。請依 [subgroup, conjugate_rows, normal, certificate] 欄序回答。

查看答案與解釋([0], [[0, [0], 是], [1, [0], 是], [2, [0], 是], [3, [0], 是]], 是, every_group_element_conjugates_H_to_itself)

Wave6第七層核對=([0], [[0, [0], 是], [1, [0], 是], [2, [0], 是], [3, [0], 是]], 是, every_group_element_conjugates_H_to_itself)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0046/)

有限正規子群 · qf-mod44-normal-conjugate-set-audit · candidate





## 47. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-conjugate-set-audit；資料={"group_table":[[2,3,4,5,0,1],[3,4,5,0,1,2],[4,5,0,1,2,3],[5,0,1,2,3,4],[0,1,2,3,4,5],[1,2,3,4,5,0]],"identity":4,"subset":[0,1,2,3,4,5]}。請依 [subgroup, conjugate_rows, normal, certificate] 欄序回答。

查看答案與解釋([0, 1, 2, 3, 4, 5], [[0, [0, 1, 2, 3, 4, 5], 是], [1, [0, 1, 2, 3, 4, 5], 是], [2, [0, 1, 2, 3, 4, 5], 是], [3, [0, 1, 2, 3, 4, 5], 是], [4, [0, 1, 2, 3, 4, 5], 是], [5, [0, 1, 2, 3, 4, 5], 是]], 是, every_group_element_conjugates_H_to_itself)

Wave6第七層核對=([0, 1, 2, 3, 4, 5], [[0, [0, 1, 2, 3, 4, 5], 是], [1, [0, 1, 2, 3, 4, 5], 是], [2, [0, 1, 2, 3, 4, 5], 是], [3, [0, 1, 2, 3, 4, 5], 是], [4, [0, 1, 2, 3, 4, 5], 是], [5, [0, 1, 2, 3, 4, 5], 是]], 是, every_group_element_conjugates_H_to_itself)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0047/)

有限正規子群 · qf-mod44-normal-conjugate-set-audit · candidate





## 48. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-conjugate-set-audit；資料={"group_table":[[4,5,6,7,0,1,2,3],[5,6,7,0,1,2,3,4],[6,7,0,1,2,3,4,5],[7,0,1,2,3,4,5,6],[0,1,2,3,4,5,6,7],[1,2,3,4,5,6,7,0],[2,3,4,5,6,7,0,1],[3,4,5,6,7,0,1,2]],"identity":4,"subset":[4]}。請依 [subgroup, conjugate_rows, normal, certificate] 欄序回答。

查看答案與解釋([4], [[0, [4], 是], [1, [4], 是], [2, [4], 是], [3, [4], 是], [4, [4], 是], [5, [4], 是], [6, [4], 是], [7, [4], 是]], 是, every_group_element_conjugates_H_to_itself)

Wave6第七層核對=([4], [[0, [4], 是], [1, [4], 是], [2, [4], 是], [3, [4], 是], [4, [4], 是], [5, [4], 是], [6, [4], 是], [7, [4], 是]], 是, every_group_element_conjugates_H_to_itself)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0048/)

有限正規子群 · qf-mod44-normal-conjugate-set-audit · candidate





## 49. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-conjugate-set-audit；資料={"group_table":[[6,7,8,9,0,1,2,3,4,5],[7,8,9,0,1,2,3,4,5,6],[8,9,0,1,2,3,4,5,6,7],[9,0,1,2,3,4,5,6,7,8],[0,1,2,3,4,5,6,7,8,9],[1,2,3,4,5,6,7,8,9,0],[2,3,4,5,6,7,8,9,0,1],[3,4,5,6,7,8,9,0,1,2],[4,5,6,7,8,9,0,1,2,3],[5,6,7,8,9,0,1,2,3,4]],"identity":4,"subset":[0,1,2,3,4,5,6,7,8,9]}。請依 [subgroup, conjugate_rows, normal, certificate] 欄序回答。

查看答案與解釋([0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [[0, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [1, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [2, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [3, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [4, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [5, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [6, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [7, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [8, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [9, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是]], 是, every_group_element_conjugates_H_to_itself)

Wave6第七層核對=([0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [[0, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [1, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [2, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [3, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [4, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [5, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [6, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [7, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [8, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [9, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是]], 是, every_group_element_conjugates_H_to_itself)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0049/)

有限正規子群 · qf-mod44-normal-conjugate-set-audit · candidate





## 50. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-conjugate-set-audit；資料={"group_table":[[8,9,10,11,0,1,2,3,4,5,6,7],[9,10,11,0,1,2,3,4,5,6,7,8],[10,11,0,1,2,3,4,5,6,7,8,9],[11,0,1,2,3,4,5,6,7,8,9,10],[0,1,2,3,4,5,6,7,8,9,10,11],[1,2,3,4,5,6,7,8,9,10,11,0],[2,3,4,5,6,7,8,9,10,11,0,1],[3,4,5,6,7,8,9,10,11,0,1,2],[4,5,6,7,8,9,10,11,0,1,2,3],[5,6,7,8,9,10,11,0,1,2,3,4],[6,7,8,9,10,11,0,1,2,3,4,5],[7,8,9,10,11,0,1,2,3,4,5,6]],"identity":4,"subset":[4]}。請依 [subgroup, conjugate_rows, normal, certificate] 欄序回答。

查看答案與解釋([4], [[0, [4], 是], [1, [4], 是], [2, [4], 是], [3, [4], 是], [4, [4], 是], [5, [4], 是], [6, [4], 是], [7, [4], 是], [8, [4], 是], [9, [4], 是], [10, [4], 是], [11, [4], 是]], 是, every_group_element_conjugates_H_to_itself)

Wave6第七層核對=([4], [[0, [4], 是], [1, [4], 是], [2, [4], 是], [3, [4], 是], [4, [4], 是], [5, [4], 是], [6, [4], 是], [7, [4], 是], [8, [4], 是], [9, [4], 是], [10, [4], 是], [11, [4], 是]], 是, every_group_element_conjugates_H_to_itself)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0050/)

有限正規子群 · qf-mod44-normal-conjugate-set-audit · candidate





## 51. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-left-right-coset-audit；資料={"group_table":[[0,1,2,3],[1,2,3,0],[2,3,0,1],[3,0,1,2]],"identity":0,"subset":[0]}。請依 [subgroup, coset_rows, all_left_right_equal, certificate] 欄序回答。

查看答案與解釋([0], [[0, [0], [0], 是], [1, [1], [1], 是], [2, [2], [2], 是], [3, [3], [3], 是]], 是, left_and_right_cosets_agree_for_every_g_exactly_when_H_is_normal)

Wave6第七層核對=([0], [[0, [0], [0], 是], [1, [1], [1], 是], [2, [2], [2], 是], [3, [3], [3], 是]], 是, left_and_right_cosets_agree_for_every_g_exactly_when_H_is_normal)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0051/)

有限正規子群 · qf-mod44-normal-left-right-coset-audit · candidate





## 52. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-left-right-coset-audit；資料={"group_table":[[0,1,2,3,4,5],[1,2,3,4,5,0],[2,3,4,5,0,1],[3,4,5,0,1,2],[4,5,0,1,2,3],[5,0,1,2,3,4]],"identity":0,"subset":[0,1,2,3,4,5]}。請依 [subgroup, coset_rows, all_left_right_equal, certificate] 欄序回答。

查看答案與解釋([0, 1, 2, 3, 4, 5], [[0, [0, 1, 2, 3, 4, 5], [0, 1, 2, 3, 4, 5], 是], [1, [0, 1, 2, 3, 4, 5], [0, 1, 2, 3, 4, 5], 是], [2, [0, 1, 2, 3, 4, 5], [0, 1, 2, 3, 4, 5], 是], [3, [0, 1, 2, 3, 4, 5], [0, 1, 2, 3, 4, 5], 是], [4, [0, 1, 2, 3, 4, 5], [0, 1, 2, 3, 4, 5], 是], [5, [0, 1, 2, 3, 4, 5], [0, 1, 2, 3, 4, 5], 是]], 是, left_and_right_cosets_agree_for_every_g_exactly_when_H_is_normal)

Wave6第七層核對=([0, 1, 2, 3, 4, 5], [[0, [0, 1, 2, 3, 4, 5], [0, 1, 2, 3, 4, 5], 是], [1, [0, 1, 2, 3, 4, 5], [0, 1, 2, 3, 4, 5], 是], [2, [0, 1, 2, 3, 4, 5], [0, 1, 2, 3, 4, 5], 是], [3, [0, 1, 2, 3, 4, 5], [0, 1, 2, 3, 4, 5], 是], [4, [0, 1, 2, 3, 4, 5], [0, 1, 2, 3, 4, 5], 是], [5, [0, 1, 2, 3, 4, 5], [0, 1, 2, 3, 4, 5], 是]], 是, left_and_right_cosets_agree_for_every_g_exactly_when_H_is_normal)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0052/)

有限正規子群 · qf-mod44-normal-left-right-coset-audit · candidate





## 53. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-left-right-coset-audit；資料={"group_table":[[0,1,2,3,4,5,6,7],[1,2,3,4,5,6,7,0],[2,3,4,5,6,7,0,1],[3,4,5,6,7,0,1,2],[4,5,6,7,0,1,2,3],[5,6,7,0,1,2,3,4],[6,7,0,1,2,3,4,5],[7,0,1,2,3,4,5,6]],"identity":0,"subset":[0]}。請依 [subgroup, coset_rows, all_left_right_equal, certificate] 欄序回答。

查看答案與解釋([0], [[0, [0], [0], 是], [1, [1], [1], 是], [2, [2], [2], 是], [3, [3], [3], 是], [4, [4], [4], 是], [5, [5], [5], 是], [6, [6], [6], 是], [7, [7], [7], 是]], 是, left_and_right_cosets_agree_for_every_g_exactly_when_H_is_normal)

Wave6第七層核對=([0], [[0, [0], [0], 是], [1, [1], [1], 是], [2, [2], [2], 是], [3, [3], [3], 是], [4, [4], [4], 是], [5, [5], [5], 是], [6, [6], [6], 是], [7, [7], [7], 是]], 是, left_and_right_cosets_agree_for_every_g_exactly_when_H_is_normal)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0053/)

有限正規子群 · qf-mod44-normal-left-right-coset-audit · candidate





## 54. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-left-right-coset-audit；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9],[1,2,3,4,5,6,7,8,9,0],[2,3,4,5,6,7,8,9,0,1],[3,4,5,6,7,8,9,0,1,2],[4,5,6,7,8,9,0,1,2,3],[5,6,7,8,9,0,1,2,3,4],[6,7,8,9,0,1,2,3,4,5],[7,8,9,0,1,2,3,4,5,6],[8,9,0,1,2,3,4,5,6,7],[9,0,1,2,3,4,5,6,7,8]],"identity":0,"subset":[0,1,2,3,4,5,6,7,8,9]}。請依 [subgroup, coset_rows, all_left_right_equal, certificate] 欄序回答。

查看答案與解釋([0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [[0, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [1, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [2, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [3, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [4, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [5, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [6, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [7, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [8, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [9, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是]], 是, left_and_right_cosets_agree_for_every_g_exactly_when_H_is_normal)

Wave6第七層核對=([0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [[0, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [1, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [2, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [3, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [4, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [5, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [6, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [7, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [8, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [9, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是]], 是, left_and_right_cosets_agree_for_every_g_exactly_when_H_is_normal)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0054/)

有限正規子群 · qf-mod44-normal-left-right-coset-audit · candidate





## 55. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-left-right-coset-audit；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11],[1,2,3,4,5,6,7,8,9,10,11,0],[2,3,4,5,6,7,8,9,10,11,0,1],[3,4,5,6,7,8,9,10,11,0,1,2],[4,5,6,7,8,9,10,11,0,1,2,3],[5,6,7,8,9,10,11,0,1,2,3,4],[6,7,8,9,10,11,0,1,2,3,4,5],[7,8,9,10,11,0,1,2,3,4,5,6],[8,9,10,11,0,1,2,3,4,5,6,7],[9,10,11,0,1,2,3,4,5,6,7,8],[10,11,0,1,2,3,4,5,6,7,8,9],[11,0,1,2,3,4,5,6,7,8,9,10]],"identity":0,"subset":[0]}。請依 [subgroup, coset_rows, all_left_right_equal, certificate] 欄序回答。

查看答案與解釋([0], [[0, [0], [0], 是], [1, [1], [1], 是], [2, [2], [2], 是], [3, [3], [3], 是], [4, [4], [4], 是], [5, [5], [5], 是], [6, [6], [6], 是], [7, [7], [7], 是], [8, [8], [8], 是], [9, [9], [9], 是], [10, [10], [10], 是], [11, [11], [11], 是]], 是, left_and_right_cosets_agree_for_every_g_exactly_when_H_is_normal)

Wave6第七層核對=([0], [[0, [0], [0], 是], [1, [1], [1], 是], [2, [2], [2], 是], [3, [3], [3], 是], [4, [4], [4], 是], [5, [5], [5], 是], [6, [6], [6], 是], [7, [7], [7], 是], [8, [8], [8], 是], [9, [9], [9], 是], [10, [10], [10], 是], [11, [11], [11], 是]], 是, left_and_right_cosets_agree_for_every_g_exactly_when_H_is_normal)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0055/)

有限正規子群 · qf-mod44-normal-left-right-coset-audit · candidate





## 56. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-left-right-coset-audit；資料={"group_table":[[3,0,1,2],[0,1,2,3],[1,2,3,0],[2,3,0,1]],"identity":1,"subset":[0,1,2,3]}。請依 [subgroup, coset_rows, all_left_right_equal, certificate] 欄序回答。

查看答案與解釋([0, 1, 2, 3], [[0, [0, 1, 2, 3], [0, 1, 2, 3], 是], [1, [0, 1, 2, 3], [0, 1, 2, 3], 是], [2, [0, 1, 2, 3], [0, 1, 2, 3], 是], [3, [0, 1, 2, 3], [0, 1, 2, 3], 是]], 是, left_and_right_cosets_agree_for_every_g_exactly_when_H_is_normal)

Wave6第七層核對=([0, 1, 2, 3], [[0, [0, 1, 2, 3], [0, 1, 2, 3], 是], [1, [0, 1, 2, 3], [0, 1, 2, 3], 是], [2, [0, 1, 2, 3], [0, 1, 2, 3], 是], [3, [0, 1, 2, 3], [0, 1, 2, 3], 是]], 是, left_and_right_cosets_agree_for_every_g_exactly_when_H_is_normal)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0056/)

有限正規子群 · qf-mod44-normal-left-right-coset-audit · candidate





## 57. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-left-right-coset-audit；資料={"group_table":[[5,0,1,2,3,4],[0,1,2,3,4,5],[1,2,3,4,5,0],[2,3,4,5,0,1],[3,4,5,0,1,2],[4,5,0,1,2,3]],"identity":1,"subset":[1]}。請依 [subgroup, coset_rows, all_left_right_equal, certificate] 欄序回答。

查看答案與解釋([1], [[0, [0], [0], 是], [1, [1], [1], 是], [2, [2], [2], 是], [3, [3], [3], 是], [4, [4], [4], 是], [5, [5], [5], 是]], 是, left_and_right_cosets_agree_for_every_g_exactly_when_H_is_normal)

Wave6第七層核對=([1], [[0, [0], [0], 是], [1, [1], [1], 是], [2, [2], [2], 是], [3, [3], [3], 是], [4, [4], [4], 是], [5, [5], [5], 是]], 是, left_and_right_cosets_agree_for_every_g_exactly_when_H_is_normal)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0057/)

有限正規子群 · qf-mod44-normal-left-right-coset-audit · candidate





## 58. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-left-right-coset-audit；資料={"group_table":[[7,0,1,2,3,4,5,6],[0,1,2,3,4,5,6,7],[1,2,3,4,5,6,7,0],[2,3,4,5,6,7,0,1],[3,4,5,6,7,0,1,2],[4,5,6,7,0,1,2,3],[5,6,7,0,1,2,3,4],[6,7,0,1,2,3,4,5]],"identity":1,"subset":[0,1,2,3,4,5,6,7]}。請依 [subgroup, coset_rows, all_left_right_equal, certificate] 欄序回答。

查看答案與解釋([0, 1, 2, 3, 4, 5, 6, 7], [[0, [0, 1, 2, 3, 4, 5, 6, 7], [0, 1, 2, 3, 4, 5, 6, 7], 是], [1, [0, 1, 2, 3, 4, 5, 6, 7], [0, 1, 2, 3, 4, 5, 6, 7], 是], [2, [0, 1, 2, 3, 4, 5, 6, 7], [0, 1, 2, 3, 4, 5, 6, 7], 是], [3, [0, 1, 2, 3, 4, 5, 6, 7], [0, 1, 2, 3, 4, 5, 6, 7], 是], [4, [0, 1, 2, 3, 4, 5, 6, 7], [0, 1, 2, 3, 4, 5, 6, 7], 是], [5, [0, 1, 2, 3, 4, 5, 6, 7], [0, 1, 2, 3, 4, 5, 6, 7], 是], [6, [0, 1, 2, 3, 4, 5, 6, 7], [0, 1, 2, 3, 4, 5, 6, 7], 是], [7, [0, 1, 2, 3, 4, 5, 6, 7], [0, 1, 2, 3, 4, 5, 6, 7], 是]], 是, left_and_right_cosets_agree_for_every_g_exactly_when_H_is_normal)

Wave6第七層核對=([0, 1, 2, 3, 4, 5, 6, 7], [[0, [0, 1, 2, 3, 4, 5, 6, 7], [0, 1, 2, 3, 4, 5, 6, 7], 是], [1, [0, 1, 2, 3, 4, 5, 6, 7], [0, 1, 2, 3, 4, 5, 6, 7], 是], [2, [0, 1, 2, 3, 4, 5, 6, 7], [0, 1, 2, 3, 4, 5, 6, 7], 是], [3, [0, 1, 2, 3, 4, 5, 6, 7], [0, 1, 2, 3, 4, 5, 6, 7], 是], [4, [0, 1, 2, 3, 4, 5, 6, 7], [0, 1, 2, 3, 4, 5, 6, 7], 是], [5, [0, 1, 2, 3, 4, 5, 6, 7], [0, 1, 2, 3, 4, 5, 6, 7], 是], [6, [0, 1, 2, 3, 4, 5, 6, 7], [0, 1, 2, 3, 4, 5, 6, 7], 是], [7, [0, 1, 2, 3, 4, 5, 6, 7], [0, 1, 2, 3, 4, 5, 6, 7], 是]], 是, left_and_right_cosets_agree_for_every_g_exactly_when_H_is_normal)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0058/)

有限正規子群 · qf-mod44-normal-left-right-coset-audit · candidate





## 59. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-left-right-coset-audit；資料={"group_table":[[9,0,1,2,3,4,5,6,7,8],[0,1,2,3,4,5,6,7,8,9],[1,2,3,4,5,6,7,8,9,0],[2,3,4,5,6,7,8,9,0,1],[3,4,5,6,7,8,9,0,1,2],[4,5,6,7,8,9,0,1,2,3],[5,6,7,8,9,0,1,2,3,4],[6,7,8,9,0,1,2,3,4,5],[7,8,9,0,1,2,3,4,5,6],[8,9,0,1,2,3,4,5,6,7]],"identity":1,"subset":[1]}。請依 [subgroup, coset_rows, all_left_right_equal, certificate] 欄序回答。

查看答案與解釋([1], [[0, [0], [0], 是], [1, [1], [1], 是], [2, [2], [2], 是], [3, [3], [3], 是], [4, [4], [4], 是], [5, [5], [5], 是], [6, [6], [6], 是], [7, [7], [7], 是], [8, [8], [8], 是], [9, [9], [9], 是]], 是, left_and_right_cosets_agree_for_every_g_exactly_when_H_is_normal)

Wave6第七層核對=([1], [[0, [0], [0], 是], [1, [1], [1], 是], [2, [2], [2], 是], [3, [3], [3], 是], [4, [4], [4], 是], [5, [5], [5], 是], [6, [6], [6], 是], [7, [7], [7], 是], [8, [8], [8], 是], [9, [9], [9], 是]], 是, left_and_right_cosets_agree_for_every_g_exactly_when_H_is_normal)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0059/)

有限正規子群 · qf-mod44-normal-left-right-coset-audit · candidate





## 60. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-left-right-coset-audit；資料={"group_table":[[11,0,1,2,3,4,5,6,7,8,9,10],[0,1,2,3,4,5,6,7,8,9,10,11],[1,2,3,4,5,6,7,8,9,10,11,0],[2,3,4,5,6,7,8,9,10,11,0,1],[3,4,5,6,7,8,9,10,11,0,1,2],[4,5,6,7,8,9,10,11,0,1,2,3],[5,6,7,8,9,10,11,0,1,2,3,4],[6,7,8,9,10,11,0,1,2,3,4,5],[7,8,9,10,11,0,1,2,3,4,5,6],[8,9,10,11,0,1,2,3,4,5,6,7],[9,10,11,0,1,2,3,4,5,6,7,8],[10,11,0,1,2,3,4,5,6,7,8,9]],"identity":1,"subset":[0,1,2,3,4,5,6,7,8,9,10,11]}。請依 [subgroup, coset_rows, all_left_right_equal, certificate] 欄序回答。

查看答案與解釋([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [[0, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [1, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [2, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [3, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [4, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [5, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [6, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [7, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [8, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [9, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [10, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [11, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是]], 是, left_and_right_cosets_agree_for_every_g_exactly_when_H_is_normal)

Wave6第七層核對=([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [[0, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [1, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [2, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [3, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [4, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [5, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [6, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [7, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [8, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [9, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [10, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [11, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是]], 是, left_and_right_cosets_agree_for_every_g_exactly_when_H_is_normal)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0060/)

有限正規子群 · qf-mod44-normal-left-right-coset-audit · candidate





## 61. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-left-right-coset-audit；資料={"group_table":[[2,3,0,1],[3,0,1,2],[0,1,2,3],[1,2,3,0]],"identity":2,"subset":[2]}。請依 [subgroup, coset_rows, all_left_right_equal, certificate] 欄序回答。

查看答案與解釋([2], [[0, [0], [0], 是], [1, [1], [1], 是], [2, [2], [2], 是], [3, [3], [3], 是]], 是, left_and_right_cosets_agree_for_every_g_exactly_when_H_is_normal)

Wave6第七層核對=([2], [[0, [0], [0], 是], [1, [1], [1], 是], [2, [2], [2], 是], [3, [3], [3], 是]], 是, left_and_right_cosets_agree_for_every_g_exactly_when_H_is_normal)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0061/)

有限正規子群 · qf-mod44-normal-left-right-coset-audit · candidate





## 62. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-left-right-coset-audit；資料={"group_table":[[4,5,0,1,2,3],[5,0,1,2,3,4],[0,1,2,3,4,5],[1,2,3,4,5,0],[2,3,4,5,0,1],[3,4,5,0,1,2]],"identity":2,"subset":[0,1,2,3,4,5]}。請依 [subgroup, coset_rows, all_left_right_equal, certificate] 欄序回答。

查看答案與解釋([0, 1, 2, 3, 4, 5], [[0, [0, 1, 2, 3, 4, 5], [0, 1, 2, 3, 4, 5], 是], [1, [0, 1, 2, 3, 4, 5], [0, 1, 2, 3, 4, 5], 是], [2, [0, 1, 2, 3, 4, 5], [0, 1, 2, 3, 4, 5], 是], [3, [0, 1, 2, 3, 4, 5], [0, 1, 2, 3, 4, 5], 是], [4, [0, 1, 2, 3, 4, 5], [0, 1, 2, 3, 4, 5], 是], [5, [0, 1, 2, 3, 4, 5], [0, 1, 2, 3, 4, 5], 是]], 是, left_and_right_cosets_agree_for_every_g_exactly_when_H_is_normal)

Wave6第七層核對=([0, 1, 2, 3, 4, 5], [[0, [0, 1, 2, 3, 4, 5], [0, 1, 2, 3, 4, 5], 是], [1, [0, 1, 2, 3, 4, 5], [0, 1, 2, 3, 4, 5], 是], [2, [0, 1, 2, 3, 4, 5], [0, 1, 2, 3, 4, 5], 是], [3, [0, 1, 2, 3, 4, 5], [0, 1, 2, 3, 4, 5], 是], [4, [0, 1, 2, 3, 4, 5], [0, 1, 2, 3, 4, 5], 是], [5, [0, 1, 2, 3, 4, 5], [0, 1, 2, 3, 4, 5], 是]], 是, left_and_right_cosets_agree_for_every_g_exactly_when_H_is_normal)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0062/)

有限正規子群 · qf-mod44-normal-left-right-coset-audit · candidate





## 63. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-left-right-coset-audit；資料={"group_table":[[6,7,0,1,2,3,4,5],[7,0,1,2,3,4,5,6],[0,1,2,3,4,5,6,7],[1,2,3,4,5,6,7,0],[2,3,4,5,6,7,0,1],[3,4,5,6,7,0,1,2],[4,5,6,7,0,1,2,3],[5,6,7,0,1,2,3,4]],"identity":2,"subset":[2]}。請依 [subgroup, coset_rows, all_left_right_equal, certificate] 欄序回答。

查看答案與解釋([2], [[0, [0], [0], 是], [1, [1], [1], 是], [2, [2], [2], 是], [3, [3], [3], 是], [4, [4], [4], 是], [5, [5], [5], 是], [6, [6], [6], 是], [7, [7], [7], 是]], 是, left_and_right_cosets_agree_for_every_g_exactly_when_H_is_normal)

Wave6第七層核對=([2], [[0, [0], [0], 是], [1, [1], [1], 是], [2, [2], [2], 是], [3, [3], [3], 是], [4, [4], [4], 是], [5, [5], [5], 是], [6, [6], [6], 是], [7, [7], [7], 是]], 是, left_and_right_cosets_agree_for_every_g_exactly_when_H_is_normal)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0063/)

有限正規子群 · qf-mod44-normal-left-right-coset-audit · candidate





## 64. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-left-right-coset-audit；資料={"group_table":[[8,9,0,1,2,3,4,5,6,7],[9,0,1,2,3,4,5,6,7,8],[0,1,2,3,4,5,6,7,8,9],[1,2,3,4,5,6,7,8,9,0],[2,3,4,5,6,7,8,9,0,1],[3,4,5,6,7,8,9,0,1,2],[4,5,6,7,8,9,0,1,2,3],[5,6,7,8,9,0,1,2,3,4],[6,7,8,9,0,1,2,3,4,5],[7,8,9,0,1,2,3,4,5,6]],"identity":2,"subset":[0,1,2,3,4,5,6,7,8,9]}。請依 [subgroup, coset_rows, all_left_right_equal, certificate] 欄序回答。

查看答案與解釋([0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [[0, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [1, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [2, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [3, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [4, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [5, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [6, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [7, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [8, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [9, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是]], 是, left_and_right_cosets_agree_for_every_g_exactly_when_H_is_normal)

Wave6第七層核對=([0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [[0, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [1, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [2, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [3, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [4, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [5, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [6, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [7, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [8, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [9, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是]], 是, left_and_right_cosets_agree_for_every_g_exactly_when_H_is_normal)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0064/)

有限正規子群 · qf-mod44-normal-left-right-coset-audit · candidate





## 65. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-left-right-coset-audit；資料={"group_table":[[10,11,0,1,2,3,4,5,6,7,8,9],[11,0,1,2,3,4,5,6,7,8,9,10],[0,1,2,3,4,5,6,7,8,9,10,11],[1,2,3,4,5,6,7,8,9,10,11,0],[2,3,4,5,6,7,8,9,10,11,0,1],[3,4,5,6,7,8,9,10,11,0,1,2],[4,5,6,7,8,9,10,11,0,1,2,3],[5,6,7,8,9,10,11,0,1,2,3,4],[6,7,8,9,10,11,0,1,2,3,4,5],[7,8,9,10,11,0,1,2,3,4,5,6],[8,9,10,11,0,1,2,3,4,5,6,7],[9,10,11,0,1,2,3,4,5,6,7,8]],"identity":2,"subset":[2]}。請依 [subgroup, coset_rows, all_left_right_equal, certificate] 欄序回答。

查看答案與解釋([2], [[0, [0], [0], 是], [1, [1], [1], 是], [2, [2], [2], 是], [3, [3], [3], 是], [4, [4], [4], 是], [5, [5], [5], 是], [6, [6], [6], 是], [7, [7], [7], 是], [8, [8], [8], 是], [9, [9], [9], 是], [10, [10], [10], 是], [11, [11], [11], 是]], 是, left_and_right_cosets_agree_for_every_g_exactly_when_H_is_normal)

Wave6第七層核對=([2], [[0, [0], [0], 是], [1, [1], [1], 是], [2, [2], [2], 是], [3, [3], [3], 是], [4, [4], [4], 是], [5, [5], [5], 是], [6, [6], [6], 是], [7, [7], [7], 是], [8, [8], [8], 是], [9, [9], [9], 是], [10, [10], [10], 是], [11, [11], [11], 是]], 是, left_and_right_cosets_agree_for_every_g_exactly_when_H_is_normal)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0065/)

有限正規子群 · qf-mod44-normal-left-right-coset-audit · candidate





## 66. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-left-right-coset-audit；資料={"group_table":[[1,2,3,0],[2,3,0,1],[3,0,1,2],[0,1,2,3]],"identity":3,"subset":[0,1,2,3]}。請依 [subgroup, coset_rows, all_left_right_equal, certificate] 欄序回答。

查看答案與解釋([0, 1, 2, 3], [[0, [0, 1, 2, 3], [0, 1, 2, 3], 是], [1, [0, 1, 2, 3], [0, 1, 2, 3], 是], [2, [0, 1, 2, 3], [0, 1, 2, 3], 是], [3, [0, 1, 2, 3], [0, 1, 2, 3], 是]], 是, left_and_right_cosets_agree_for_every_g_exactly_when_H_is_normal)

Wave6第七層核對=([0, 1, 2, 3], [[0, [0, 1, 2, 3], [0, 1, 2, 3], 是], [1, [0, 1, 2, 3], [0, 1, 2, 3], 是], [2, [0, 1, 2, 3], [0, 1, 2, 3], 是], [3, [0, 1, 2, 3], [0, 1, 2, 3], 是]], 是, left_and_right_cosets_agree_for_every_g_exactly_when_H_is_normal)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0066/)

有限正規子群 · qf-mod44-normal-left-right-coset-audit · candidate





## 67. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-left-right-coset-audit；資料={"group_table":[[3,4,5,0,1,2],[4,5,0,1,2,3],[5,0,1,2,3,4],[0,1,2,3,4,5],[1,2,3,4,5,0],[2,3,4,5,0,1]],"identity":3,"subset":[3]}。請依 [subgroup, coset_rows, all_left_right_equal, certificate] 欄序回答。

查看答案與解釋([3], [[0, [0], [0], 是], [1, [1], [1], 是], [2, [2], [2], 是], [3, [3], [3], 是], [4, [4], [4], 是], [5, [5], [5], 是]], 是, left_and_right_cosets_agree_for_every_g_exactly_when_H_is_normal)

Wave6第七層核對=([3], [[0, [0], [0], 是], [1, [1], [1], 是], [2, [2], [2], 是], [3, [3], [3], 是], [4, [4], [4], 是], [5, [5], [5], 是]], 是, left_and_right_cosets_agree_for_every_g_exactly_when_H_is_normal)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0067/)

有限正規子群 · qf-mod44-normal-left-right-coset-audit · candidate





## 68. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-left-right-coset-audit；資料={"group_table":[[5,6,7,0,1,2,3,4],[6,7,0,1,2,3,4,5],[7,0,1,2,3,4,5,6],[0,1,2,3,4,5,6,7],[1,2,3,4,5,6,7,0],[2,3,4,5,6,7,0,1],[3,4,5,6,7,0,1,2],[4,5,6,7,0,1,2,3]],"identity":3,"subset":[0,1,2,3,4,5,6,7]}。請依 [subgroup, coset_rows, all_left_right_equal, certificate] 欄序回答。

查看答案與解釋([0, 1, 2, 3, 4, 5, 6, 7], [[0, [0, 1, 2, 3, 4, 5, 6, 7], [0, 1, 2, 3, 4, 5, 6, 7], 是], [1, [0, 1, 2, 3, 4, 5, 6, 7], [0, 1, 2, 3, 4, 5, 6, 7], 是], [2, [0, 1, 2, 3, 4, 5, 6, 7], [0, 1, 2, 3, 4, 5, 6, 7], 是], [3, [0, 1, 2, 3, 4, 5, 6, 7], [0, 1, 2, 3, 4, 5, 6, 7], 是], [4, [0, 1, 2, 3, 4, 5, 6, 7], [0, 1, 2, 3, 4, 5, 6, 7], 是], [5, [0, 1, 2, 3, 4, 5, 6, 7], [0, 1, 2, 3, 4, 5, 6, 7], 是], [6, [0, 1, 2, 3, 4, 5, 6, 7], [0, 1, 2, 3, 4, 5, 6, 7], 是], [7, [0, 1, 2, 3, 4, 5, 6, 7], [0, 1, 2, 3, 4, 5, 6, 7], 是]], 是, left_and_right_cosets_agree_for_every_g_exactly_when_H_is_normal)

Wave6第七層核對=([0, 1, 2, 3, 4, 5, 6, 7], [[0, [0, 1, 2, 3, 4, 5, 6, 7], [0, 1, 2, 3, 4, 5, 6, 7], 是], [1, [0, 1, 2, 3, 4, 5, 6, 7], [0, 1, 2, 3, 4, 5, 6, 7], 是], [2, [0, 1, 2, 3, 4, 5, 6, 7], [0, 1, 2, 3, 4, 5, 6, 7], 是], [3, [0, 1, 2, 3, 4, 5, 6, 7], [0, 1, 2, 3, 4, 5, 6, 7], 是], [4, [0, 1, 2, 3, 4, 5, 6, 7], [0, 1, 2, 3, 4, 5, 6, 7], 是], [5, [0, 1, 2, 3, 4, 5, 6, 7], [0, 1, 2, 3, 4, 5, 6, 7], 是], [6, [0, 1, 2, 3, 4, 5, 6, 7], [0, 1, 2, 3, 4, 5, 6, 7], 是], [7, [0, 1, 2, 3, 4, 5, 6, 7], [0, 1, 2, 3, 4, 5, 6, 7], 是]], 是, left_and_right_cosets_agree_for_every_g_exactly_when_H_is_normal)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0068/)

有限正規子群 · qf-mod44-normal-left-right-coset-audit · candidate





## 69. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-left-right-coset-audit；資料={"group_table":[[7,8,9,0,1,2,3,4,5,6],[8,9,0,1,2,3,4,5,6,7],[9,0,1,2,3,4,5,6,7,8],[0,1,2,3,4,5,6,7,8,9],[1,2,3,4,5,6,7,8,9,0],[2,3,4,5,6,7,8,9,0,1],[3,4,5,6,7,8,9,0,1,2],[4,5,6,7,8,9,0,1,2,3],[5,6,7,8,9,0,1,2,3,4],[6,7,8,9,0,1,2,3,4,5]],"identity":3,"subset":[3]}。請依 [subgroup, coset_rows, all_left_right_equal, certificate] 欄序回答。

查看答案與解釋([3], [[0, [0], [0], 是], [1, [1], [1], 是], [2, [2], [2], 是], [3, [3], [3], 是], [4, [4], [4], 是], [5, [5], [5], 是], [6, [6], [6], 是], [7, [7], [7], 是], [8, [8], [8], 是], [9, [9], [9], 是]], 是, left_and_right_cosets_agree_for_every_g_exactly_when_H_is_normal)

Wave6第七層核對=([3], [[0, [0], [0], 是], [1, [1], [1], 是], [2, [2], [2], 是], [3, [3], [3], 是], [4, [4], [4], 是], [5, [5], [5], 是], [6, [6], [6], 是], [7, [7], [7], 是], [8, [8], [8], 是], [9, [9], [9], 是]], 是, left_and_right_cosets_agree_for_every_g_exactly_when_H_is_normal)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0069/)

有限正規子群 · qf-mod44-normal-left-right-coset-audit · candidate





## 70. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-left-right-coset-audit；資料={"group_table":[[9,10,11,0,1,2,3,4,5,6,7,8],[10,11,0,1,2,3,4,5,6,7,8,9],[11,0,1,2,3,4,5,6,7,8,9,10],[0,1,2,3,4,5,6,7,8,9,10,11],[1,2,3,4,5,6,7,8,9,10,11,0],[2,3,4,5,6,7,8,9,10,11,0,1],[3,4,5,6,7,8,9,10,11,0,1,2],[4,5,6,7,8,9,10,11,0,1,2,3],[5,6,7,8,9,10,11,0,1,2,3,4],[6,7,8,9,10,11,0,1,2,3,4,5],[7,8,9,10,11,0,1,2,3,4,5,6],[8,9,10,11,0,1,2,3,4,5,6,7]],"identity":3,"subset":[0,1,2,3,4,5,6,7,8,9,10,11]}。請依 [subgroup, coset_rows, all_left_right_equal, certificate] 欄序回答。

查看答案與解釋([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [[0, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [1, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [2, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [3, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [4, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [5, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [6, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [7, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [8, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [9, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [10, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [11, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是]], 是, left_and_right_cosets_agree_for_every_g_exactly_when_H_is_normal)

Wave6第七層核對=([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [[0, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [1, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [2, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [3, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [4, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [5, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [6, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [7, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [8, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [9, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [10, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [11, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是]], 是, left_and_right_cosets_agree_for_every_g_exactly_when_H_is_normal)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0070/)

有限正規子群 · qf-mod44-normal-left-right-coset-audit · candidate





## 71. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-left-right-coset-audit；資料={"group_table":[[0,1,2,3],[1,0,3,2],[2,3,1,0],[3,2,0,1]],"identity":0,"subset":[0]}。請依 [subgroup, coset_rows, all_left_right_equal, certificate] 欄序回答。

查看答案與解釋([0], [[0, [0], [0], 是], [1, [1], [1], 是], [2, [2], [2], 是], [3, [3], [3], 是]], 是, left_and_right_cosets_agree_for_every_g_exactly_when_H_is_normal)

Wave6第七層核對=([0], [[0, [0], [0], 是], [1, [1], [1], 是], [2, [2], [2], 是], [3, [3], [3], 是]], 是, left_and_right_cosets_agree_for_every_g_exactly_when_H_is_normal)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0071/)

有限正規子群 · qf-mod44-normal-left-right-coset-audit · candidate





## 72. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-left-right-coset-audit；資料={"group_table":[[2,3,4,5,0,1],[3,4,5,0,1,2],[4,5,0,1,2,3],[5,0,1,2,3,4],[0,1,2,3,4,5],[1,2,3,4,5,0]],"identity":4,"subset":[0,1,2,3,4,5]}。請依 [subgroup, coset_rows, all_left_right_equal, certificate] 欄序回答。

查看答案與解釋([0, 1, 2, 3, 4, 5], [[0, [0, 1, 2, 3, 4, 5], [0, 1, 2, 3, 4, 5], 是], [1, [0, 1, 2, 3, 4, 5], [0, 1, 2, 3, 4, 5], 是], [2, [0, 1, 2, 3, 4, 5], [0, 1, 2, 3, 4, 5], 是], [3, [0, 1, 2, 3, 4, 5], [0, 1, 2, 3, 4, 5], 是], [4, [0, 1, 2, 3, 4, 5], [0, 1, 2, 3, 4, 5], 是], [5, [0, 1, 2, 3, 4, 5], [0, 1, 2, 3, 4, 5], 是]], 是, left_and_right_cosets_agree_for_every_g_exactly_when_H_is_normal)

Wave6第七層核對=([0, 1, 2, 3, 4, 5], [[0, [0, 1, 2, 3, 4, 5], [0, 1, 2, 3, 4, 5], 是], [1, [0, 1, 2, 3, 4, 5], [0, 1, 2, 3, 4, 5], 是], [2, [0, 1, 2, 3, 4, 5], [0, 1, 2, 3, 4, 5], 是], [3, [0, 1, 2, 3, 4, 5], [0, 1, 2, 3, 4, 5], 是], [4, [0, 1, 2, 3, 4, 5], [0, 1, 2, 3, 4, 5], 是], [5, [0, 1, 2, 3, 4, 5], [0, 1, 2, 3, 4, 5], 是]], 是, left_and_right_cosets_agree_for_every_g_exactly_when_H_is_normal)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0072/)

有限正規子群 · qf-mod44-normal-left-right-coset-audit · candidate





## 73. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-left-right-coset-audit；資料={"group_table":[[4,5,6,7,0,1,2,3],[5,6,7,0,1,2,3,4],[6,7,0,1,2,3,4,5],[7,0,1,2,3,4,5,6],[0,1,2,3,4,5,6,7],[1,2,3,4,5,6,7,0],[2,3,4,5,6,7,0,1],[3,4,5,6,7,0,1,2]],"identity":4,"subset":[4]}。請依 [subgroup, coset_rows, all_left_right_equal, certificate] 欄序回答。

查看答案與解釋([4], [[0, [0], [0], 是], [1, [1], [1], 是], [2, [2], [2], 是], [3, [3], [3], 是], [4, [4], [4], 是], [5, [5], [5], 是], [6, [6], [6], 是], [7, [7], [7], 是]], 是, left_and_right_cosets_agree_for_every_g_exactly_when_H_is_normal)

Wave6第七層核對=([4], [[0, [0], [0], 是], [1, [1], [1], 是], [2, [2], [2], 是], [3, [3], [3], 是], [4, [4], [4], 是], [5, [5], [5], 是], [6, [6], [6], 是], [7, [7], [7], 是]], 是, left_and_right_cosets_agree_for_every_g_exactly_when_H_is_normal)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0073/)

有限正規子群 · qf-mod44-normal-left-right-coset-audit · candidate





## 74. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-left-right-coset-audit；資料={"group_table":[[6,7,8,9,0,1,2,3,4,5],[7,8,9,0,1,2,3,4,5,6],[8,9,0,1,2,3,4,5,6,7],[9,0,1,2,3,4,5,6,7,8],[0,1,2,3,4,5,6,7,8,9],[1,2,3,4,5,6,7,8,9,0],[2,3,4,5,6,7,8,9,0,1],[3,4,5,6,7,8,9,0,1,2],[4,5,6,7,8,9,0,1,2,3],[5,6,7,8,9,0,1,2,3,4]],"identity":4,"subset":[0,1,2,3,4,5,6,7,8,9]}。請依 [subgroup, coset_rows, all_left_right_equal, certificate] 欄序回答。

查看答案與解釋([0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [[0, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [1, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [2, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [3, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [4, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [5, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [6, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [7, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [8, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [9, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是]], 是, left_and_right_cosets_agree_for_every_g_exactly_when_H_is_normal)

Wave6第七層核對=([0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [[0, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [1, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [2, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [3, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [4, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [5, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [6, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [7, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [8, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是], [9, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是]], 是, left_and_right_cosets_agree_for_every_g_exactly_when_H_is_normal)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0074/)

有限正規子群 · qf-mod44-normal-left-right-coset-audit · candidate





## 75. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-left-right-coset-audit；資料={"group_table":[[8,9,10,11,0,1,2,3,4,5,6,7],[9,10,11,0,1,2,3,4,5,6,7,8],[10,11,0,1,2,3,4,5,6,7,8,9],[11,0,1,2,3,4,5,6,7,8,9,10],[0,1,2,3,4,5,6,7,8,9,10,11],[1,2,3,4,5,6,7,8,9,10,11,0],[2,3,4,5,6,7,8,9,10,11,0,1],[3,4,5,6,7,8,9,10,11,0,1,2],[4,5,6,7,8,9,10,11,0,1,2,3],[5,6,7,8,9,10,11,0,1,2,3,4],[6,7,8,9,10,11,0,1,2,3,4,5],[7,8,9,10,11,0,1,2,3,4,5,6]],"identity":4,"subset":[4]}。請依 [subgroup, coset_rows, all_left_right_equal, certificate] 欄序回答。

查看答案與解釋([4], [[0, [0], [0], 是], [1, [1], [1], 是], [2, [2], [2], 是], [3, [3], [3], 是], [4, [4], [4], 是], [5, [5], [5], 是], [6, [6], [6], 是], [7, [7], [7], 是], [8, [8], [8], 是], [9, [9], [9], 是], [10, [10], [10], 是], [11, [11], [11], 是]], 是, left_and_right_cosets_agree_for_every_g_exactly_when_H_is_normal)

Wave6第七層核對=([4], [[0, [0], [0], 是], [1, [1], [1], 是], [2, [2], [2], 是], [3, [3], [3], 是], [4, [4], [4], 是], [5, [5], [5], 是], [6, [6], [6], 是], [7, [7], [7], 是], [8, [8], [8], 是], [9, [9], [9], 是], [10, [10], [10], 是], [11, [11], [11], 是]], 是, left_and_right_cosets_agree_for_every_g_exactly_when_H_is_normal)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0075/)

有限正規子群 · qf-mod44-normal-left-right-coset-audit · candidate





## 76. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-nonnormal-witness；資料={"group_table":[[0,1,2,3,4,5],[1,0,5,4,3,2],[2,4,0,5,1,3],[3,5,4,0,2,1],[4,2,3,1,5,0],[5,3,1,2,0,4]],"identity":0,"subset":[0,1],"witness_g":4,"witness_h":1}。請依 [subgroup, g, h, inverse_g, escaping_conjugate, normal, certificate] 欄序回答。

查看答案與解釋([0, 1], 4, 1, 5, 3, 否, one_h_in_H_with_g_h_g_inverse_outside_H_disproves_normality)

Wave6第七層核對=([0, 1], 4, 1, 5, 3, 否, one_h_in_H_with_g_h_g_inverse_outside_H_disproves_normality)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0076/)

有限正規子群 · qf-mod44-normal-nonnormal-witness · candidate





## 77. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-nonnormal-witness；資料={"group_table":[[0,1,2,3,4,5],[1,0,4,5,2,3],[2,5,0,4,3,1],[3,4,5,0,1,2],[4,3,1,2,5,0],[5,2,3,1,0,4]],"identity":0,"subset":[0,1],"witness_g":5,"witness_h":1}。請依 [subgroup, g, h, inverse_g, escaping_conjugate, normal, certificate] 欄序回答。

查看答案與解釋([0, 1], 5, 1, 4, 3, 否, one_h_in_H_with_g_h_g_inverse_outside_H_disproves_normality)

Wave6第七層核對=([0, 1], 5, 1, 4, 3, 否, one_h_in_H_with_g_h_g_inverse_outside_H_disproves_normality)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0077/)

有限正規子群 · qf-mod44-normal-nonnormal-witness · candidate





## 78. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-nonnormal-witness；資料={"group_table":[[0,1,2,3,4,5],[1,0,5,4,3,2],[2,3,0,1,5,4],[3,2,4,5,1,0],[4,5,3,2,0,1],[5,4,1,0,2,3]],"identity":0,"subset":[0,1],"witness_g":3,"witness_h":1}。請依 [subgroup, g, h, inverse_g, escaping_conjugate, normal, certificate] 欄序回答。

查看答案與解釋([0, 1], 3, 1, 5, 4, 否, one_h_in_H_with_g_h_g_inverse_outside_H_disproves_normality)

Wave6第七層核對=([0, 1], 3, 1, 5, 4, 否, one_h_in_H_with_g_h_g_inverse_outside_H_disproves_normality)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0078/)

有限正規子群 · qf-mod44-normal-nonnormal-witness · candidate





## 79. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-nonnormal-witness；資料={"group_table":[[0,1,2,3,4,5],[1,0,3,2,5,4],[2,5,0,4,3,1],[3,4,1,5,2,0],[4,3,5,1,0,2],[5,2,4,0,1,3]],"identity":0,"subset":[0,1],"witness_g":5,"witness_h":1}。請依 [subgroup, g, h, inverse_g, escaping_conjugate, normal, certificate] 欄序回答。

查看答案與解釋([0, 1], 5, 1, 3, 4, 否, one_h_in_H_with_g_h_g_inverse_outside_H_disproves_normality)

Wave6第七層核對=([0, 1], 5, 1, 3, 4, 否, one_h_in_H_with_g_h_g_inverse_outside_H_disproves_normality)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0079/)

有限正規子群 · qf-mod44-normal-nonnormal-witness · candidate





## 80. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-nonnormal-witness；資料={"group_table":[[0,1,2,3,4,5],[1,0,4,5,2,3],[2,3,0,1,5,4],[3,2,5,4,0,1],[4,5,1,0,3,2],[5,4,3,2,1,0]],"identity":0,"subset":[0,1],"witness_g":3,"witness_h":1}。請依 [subgroup, g, h, inverse_g, escaping_conjugate, normal, certificate] 欄序回答。

查看答案與解釋([0, 1], 3, 1, 4, 5, 否, one_h_in_H_with_g_h_g_inverse_outside_H_disproves_normality)

Wave6第七層核對=([0, 1], 3, 1, 4, 5, 否, one_h_in_H_with_g_h_g_inverse_outside_H_disproves_normality)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0080/)

有限正規子群 · qf-mod44-normal-nonnormal-witness · candidate





## 81. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-nonnormal-witness；資料={"group_table":[[0,1,2,3,4,5],[1,0,3,2,5,4],[2,4,0,5,1,3],[3,5,1,4,0,2],[4,2,5,0,3,1],[5,3,4,1,2,0]],"identity":0,"subset":[0,1],"witness_g":4,"witness_h":1}。請依 [subgroup, g, h, inverse_g, escaping_conjugate, normal, certificate] 欄序回答。

查看答案與解釋([0, 1], 4, 1, 3, 5, 否, one_h_in_H_with_g_h_g_inverse_outside_H_disproves_normality)

Wave6第七層核對=([0, 1], 4, 1, 3, 5, 否, one_h_in_H_with_g_h_g_inverse_outside_H_disproves_normality)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0081/)

有限正規子群 · qf-mod44-normal-nonnormal-witness · candidate





## 82. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-nonnormal-witness；資料={"group_table":[[0,1,2,3,4,5],[1,0,4,5,2,3],[2,5,0,4,3,1],[3,4,5,0,1,2],[4,3,1,2,5,0],[5,2,3,1,0,4]],"identity":0,"subset":[0,1],"witness_g":4,"witness_h":1}。請依 [subgroup, g, h, inverse_g, escaping_conjugate, normal, certificate] 欄序回答。

查看答案與解釋([0, 1], 4, 1, 5, 2, 否, one_h_in_H_with_g_h_g_inverse_outside_H_disproves_normality)

Wave6第七層核對=([0, 1], 4, 1, 5, 2, 否, one_h_in_H_with_g_h_g_inverse_outside_H_disproves_normality)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0082/)

有限正規子群 · qf-mod44-normal-nonnormal-witness · candidate





## 83. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-nonnormal-witness；資料={"group_table":[[0,1,2,3,4,5],[1,0,5,4,3,2],[2,4,0,5,1,3],[3,5,4,0,2,1],[4,2,3,1,5,0],[5,3,1,2,0,4]],"identity":0,"subset":[0,1],"witness_g":5,"witness_h":1}。請依 [subgroup, g, h, inverse_g, escaping_conjugate, normal, certificate] 欄序回答。

查看答案與解釋([0, 1], 5, 1, 4, 2, 否, one_h_in_H_with_g_h_g_inverse_outside_H_disproves_normality)

Wave6第七層核對=([0, 1], 5, 1, 4, 2, 否, one_h_in_H_with_g_h_g_inverse_outside_H_disproves_normality)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0083/)

有限正規子群 · qf-mod44-normal-nonnormal-witness · candidate





## 84. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-nonnormal-witness；資料={"group_table":[[0,1,2,3,4,5],[1,0,4,5,2,3],[2,3,5,4,1,0],[3,2,1,0,5,4],[4,5,3,2,0,1],[5,4,0,1,3,2]],"identity":0,"subset":[0,1],"witness_g":2,"witness_h":1}。請依 [subgroup, g, h, inverse_g, escaping_conjugate, normal, certificate] 欄序回答。

查看答案與解釋([0, 1], 2, 1, 5, 4, 否, one_h_in_H_with_g_h_g_inverse_outside_H_disproves_normality)

Wave6第七層核對=([0, 1], 2, 1, 5, 4, 否, one_h_in_H_with_g_h_g_inverse_outside_H_disproves_normality)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0084/)

有限正規子群 · qf-mod44-normal-nonnormal-witness · candidate





## 85. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-nonnormal-witness；資料={"group_table":[[0,1,2,3,4,5],[1,0,3,2,5,4],[2,4,5,1,3,0],[3,5,4,0,2,1],[4,2,1,5,0,3],[5,3,0,4,1,2]],"identity":0,"subset":[0,1],"witness_g":5,"witness_h":1}。請依 [subgroup, g, h, inverse_g, escaping_conjugate, normal, certificate] 欄序回答。

查看答案與解釋([0, 1], 5, 1, 2, 4, 否, one_h_in_H_with_g_h_g_inverse_outside_H_disproves_normality)

Wave6第七層核對=([0, 1], 5, 1, 2, 4, 否, one_h_in_H_with_g_h_g_inverse_outside_H_disproves_normality)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0085/)

有限正規子群 · qf-mod44-normal-nonnormal-witness · candidate





## 86. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-nonnormal-witness；資料={"group_table":[[0,1,2,3,4,5],[1,0,5,4,3,2],[2,3,4,5,0,1],[3,2,1,0,5,4],[4,5,0,1,2,3],[5,4,3,2,1,0]],"identity":0,"subset":[0,1],"witness_g":2,"witness_h":1}。請依 [subgroup, g, h, inverse_g, escaping_conjugate, normal, certificate] 欄序回答。

查看答案與解釋([0, 1], 2, 1, 4, 5, 否, one_h_in_H_with_g_h_g_inverse_outside_H_disproves_normality)

Wave6第七層核對=([0, 1], 2, 1, 4, 5, 否, one_h_in_H_with_g_h_g_inverse_outside_H_disproves_normality)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0086/)

有限正規子群 · qf-mod44-normal-nonnormal-witness · candidate





## 87. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-nonnormal-witness；資料={"group_table":[[0,1,2,3,4,5],[1,0,3,2,5,4],[2,5,4,1,0,3],[3,4,5,0,1,2],[4,3,0,5,2,1],[5,2,1,4,3,0]],"identity":0,"subset":[0,1],"witness_g":4,"witness_h":1}。請依 [subgroup, g, h, inverse_g, escaping_conjugate, normal, certificate] 欄序回答。

查看答案與解釋([0, 1], 4, 1, 2, 5, 否, one_h_in_H_with_g_h_g_inverse_outside_H_disproves_normality)

Wave6第七層核對=([0, 1], 4, 1, 2, 5, 否, one_h_in_H_with_g_h_g_inverse_outside_H_disproves_normality)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0087/)

有限正規子群 · qf-mod44-normal-nonnormal-witness · candidate





## 88. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-nonnormal-witness；資料={"group_table":[[0,1,2,3,4,5],[1,0,3,2,5,4],[2,5,0,4,3,1],[3,4,1,5,2,0],[4,3,5,1,0,2],[5,2,4,0,1,3]],"identity":0,"subset":[0,1],"witness_g":3,"witness_h":1}。請依 [subgroup, g, h, inverse_g, escaping_conjugate, normal, certificate] 欄序回答。

查看答案與解釋([0, 1], 3, 1, 5, 2, 否, one_h_in_H_with_g_h_g_inverse_outside_H_disproves_normality)

Wave6第七層核對=([0, 1], 3, 1, 5, 2, 否, one_h_in_H_with_g_h_g_inverse_outside_H_disproves_normality)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0088/)

有限正規子群 · qf-mod44-normal-nonnormal-witness · candidate





## 89. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-nonnormal-witness；資料={"group_table":[[0,1,2,3,4,5],[1,0,5,4,3,2],[2,3,0,1,5,4],[3,2,4,5,1,0],[4,5,3,2,0,1],[5,4,1,0,2,3]],"identity":0,"subset":[0,1],"witness_g":5,"witness_h":1}。請依 [subgroup, g, h, inverse_g, escaping_conjugate, normal, certificate] 欄序回答。

查看答案與解釋([0, 1], 5, 1, 3, 2, 否, one_h_in_H_with_g_h_g_inverse_outside_H_disproves_normality)

Wave6第七層核對=([0, 1], 5, 1, 3, 2, 否, one_h_in_H_with_g_h_g_inverse_outside_H_disproves_normality)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0089/)

有限正規子群 · qf-mod44-normal-nonnormal-witness · candidate





## 90. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-nonnormal-witness；資料={"group_table":[[0,1,2,3,4,5],[1,0,3,2,5,4],[2,4,5,1,3,0],[3,5,4,0,2,1],[4,2,1,5,0,3],[5,3,0,4,1,2]],"identity":0,"subset":[0,1],"witness_g":2,"witness_h":1}。請依 [subgroup, g, h, inverse_g, escaping_conjugate, normal, certificate] 欄序回答。

查看答案與解釋([0, 1], 2, 1, 5, 3, 否, one_h_in_H_with_g_h_g_inverse_outside_H_disproves_normality)

Wave6第七層核對=([0, 1], 2, 1, 5, 3, 否, one_h_in_H_with_g_h_g_inverse_outside_H_disproves_normality)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0090/)

有限正規子群 · qf-mod44-normal-nonnormal-witness · candidate





## 91. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-nonnormal-witness；資料={"group_table":[[0,1,2,3,4,5],[1,0,4,5,2,3],[2,3,5,4,1,0],[3,2,1,0,5,4],[4,5,3,2,0,1],[5,4,0,1,3,2]],"identity":0,"subset":[0,1],"witness_g":5,"witness_h":1}。請依 [subgroup, g, h, inverse_g, escaping_conjugate, normal, certificate] 欄序回答。

查看答案與解釋([0, 1], 5, 1, 2, 3, 否, one_h_in_H_with_g_h_g_inverse_outside_H_disproves_normality)

Wave6第七層核對=([0, 1], 5, 1, 2, 3, 否, one_h_in_H_with_g_h_g_inverse_outside_H_disproves_normality)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0091/)

有限正規子群 · qf-mod44-normal-nonnormal-witness · candidate





## 92. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-nonnormal-witness；資料={"group_table":[[0,1,2,3,4,5],[1,0,5,4,3,2],[2,4,3,0,5,1],[3,5,0,2,1,4],[4,2,1,5,0,3],[5,3,4,1,2,0]],"identity":0,"subset":[0,1],"witness_g":2,"witness_h":1}。請依 [subgroup, g, h, inverse_g, escaping_conjugate, normal, certificate] 欄序回答。

查看答案與解釋([0, 1], 2, 1, 3, 5, 否, one_h_in_H_with_g_h_g_inverse_outside_H_disproves_normality)

Wave6第七層核對=([0, 1], 2, 1, 3, 5, 否, one_h_in_H_with_g_h_g_inverse_outside_H_disproves_normality)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0092/)

有限正規子群 · qf-mod44-normal-nonnormal-witness · candidate





## 93. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-nonnormal-witness；資料={"group_table":[[0,1,2,3,4,5],[1,0,4,5,2,3],[2,5,3,0,1,4],[3,4,0,2,5,1],[4,3,5,1,0,2],[5,2,1,4,3,0]],"identity":0,"subset":[0,1],"witness_g":3,"witness_h":1}。請依 [subgroup, g, h, inverse_g, escaping_conjugate, normal, certificate] 欄序回答。

查看答案與解釋([0, 1], 3, 1, 2, 5, 否, one_h_in_H_with_g_h_g_inverse_outside_H_disproves_normality)

Wave6第七層核對=([0, 1], 3, 1, 2, 5, 否, one_h_in_H_with_g_h_g_inverse_outside_H_disproves_normality)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0093/)

有限正規子群 · qf-mod44-normal-nonnormal-witness · candidate





## 94. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-nonnormal-witness；資料={"group_table":[[0,1,2,3,4,5],[1,0,3,2,5,4],[2,4,0,5,1,3],[3,5,1,4,0,2],[4,2,5,0,3,1],[5,3,4,1,2,0]],"identity":0,"subset":[0,1],"witness_g":3,"witness_h":1}。請依 [subgroup, g, h, inverse_g, escaping_conjugate, normal, certificate] 欄序回答。

查看答案與解釋([0, 1], 3, 1, 4, 2, 否, one_h_in_H_with_g_h_g_inverse_outside_H_disproves_normality)

Wave6第七層核對=([0, 1], 3, 1, 4, 2, 否, one_h_in_H_with_g_h_g_inverse_outside_H_disproves_normality)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0094/)

有限正規子群 · qf-mod44-normal-nonnormal-witness · candidate





## 95. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-nonnormal-witness；資料={"group_table":[[0,1,2,3,4,5],[1,0,4,5,2,3],[2,3,0,1,5,4],[3,2,5,4,0,1],[4,5,1,0,3,2],[5,4,3,2,1,0]],"identity":0,"subset":[0,1],"witness_g":4,"witness_h":1}。請依 [subgroup, g, h, inverse_g, escaping_conjugate, normal, certificate] 欄序回答。

查看答案與解釋([0, 1], 4, 1, 3, 2, 否, one_h_in_H_with_g_h_g_inverse_outside_H_disproves_normality)

Wave6第七層核對=([0, 1], 4, 1, 3, 2, 否, one_h_in_H_with_g_h_g_inverse_outside_H_disproves_normality)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0095/)

有限正規子群 · qf-mod44-normal-nonnormal-witness · candidate





## 96. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-nonnormal-witness；資料={"group_table":[[0,1,2,3,4,5],[1,0,3,2,5,4],[2,5,4,1,0,3],[3,4,5,0,1,2],[4,3,0,5,2,1],[5,2,1,4,3,0]],"identity":0,"subset":[0,1],"witness_g":2,"witness_h":1}。請依 [subgroup, g, h, inverse_g, escaping_conjugate, normal, certificate] 欄序回答。

查看答案與解釋([0, 1], 2, 1, 4, 3, 否, one_h_in_H_with_g_h_g_inverse_outside_H_disproves_normality)

Wave6第七層核對=([0, 1], 2, 1, 4, 3, 否, one_h_in_H_with_g_h_g_inverse_outside_H_disproves_normality)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0096/)

有限正規子群 · qf-mod44-normal-nonnormal-witness · candidate





## 97. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-nonnormal-witness；資料={"group_table":[[0,1,2,3,4,5],[1,0,5,4,3,2],[2,3,4,5,0,1],[3,2,1,0,5,4],[4,5,0,1,2,3],[5,4,3,2,1,0]],"identity":0,"subset":[0,1],"witness_g":4,"witness_h":1}。請依 [subgroup, g, h, inverse_g, escaping_conjugate, normal, certificate] 欄序回答。

查看答案與解釋([0, 1], 4, 1, 2, 3, 否, one_h_in_H_with_g_h_g_inverse_outside_H_disproves_normality)

Wave6第七層核對=([0, 1], 4, 1, 2, 3, 否, one_h_in_H_with_g_h_g_inverse_outside_H_disproves_normality)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0097/)

有限正規子群 · qf-mod44-normal-nonnormal-witness · candidate





## 98. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-nonnormal-witness；資料={"group_table":[[0,1,2,3,4,5],[1,0,4,5,2,3],[2,5,3,0,1,4],[3,4,0,2,5,1],[4,3,5,1,0,2],[5,2,1,4,3,0]],"identity":0,"subset":[0,1],"witness_g":2,"witness_h":1}。請依 [subgroup, g, h, inverse_g, escaping_conjugate, normal, certificate] 欄序回答。

查看答案與解釋([0, 1], 2, 1, 3, 4, 否, one_h_in_H_with_g_h_g_inverse_outside_H_disproves_normality)

Wave6第七層核對=([0, 1], 2, 1, 3, 4, 否, one_h_in_H_with_g_h_g_inverse_outside_H_disproves_normality)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0098/)

有限正規子群 · qf-mod44-normal-nonnormal-witness · candidate





## 99. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-nonnormal-witness；資料={"group_table":[[0,1,2,3,4,5],[1,0,5,4,3,2],[2,4,3,0,5,1],[3,5,0,2,1,4],[4,2,1,5,0,3],[5,3,4,1,2,0]],"identity":0,"subset":[0,1],"witness_g":3,"witness_h":1}。請依 [subgroup, g, h, inverse_g, escaping_conjugate, normal, certificate] 欄序回答。

查看答案與解釋([0, 1], 3, 1, 2, 4, 否, one_h_in_H_with_g_h_g_inverse_outside_H_disproves_normality)

Wave6第七層核對=([0, 1], 3, 1, 2, 4, 否, one_h_in_H_with_g_h_g_inverse_outside_H_disproves_normality)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r01-finite-normal-subgroup-0099/)

有限正規子群 · qf-mod44-normal-nonnormal-witness · candidate





## 100. 有限正規子群

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-nonnormal-witness；資料={"group_table":[[0,1,2,3,4,5],[1,0,4,5,2,3],[2,5,0,4,3,1],[3,4,5,0,1,2],[4,3,1,2,5,0],[5,2,3,1,0,4]],"identity":0,"subset":[0,2],"witness_g":4,"witness_h":2}。請依 [subgroup, g, h, inverse_g, escaping_conjugate, normal, certificate] 欄序回答。

查看答案與解釋([0, 2], 4, 2, 5, 3, 否, one_h_in_H_with_g_h_g_inverse_outside_H_disproves_normality)

Wave6第七層核對=([0, 2], 4, 2, 5, 3, 否, one_h_in_H_with_g_h_g_inverse_outside_H_disproves_normality)；依完整明示資料獨立重算；normal必須完整驗gHg^-1=H或逐g左／右陪集相等；trivial與whole subgroup保留；抽樣共軛、有限性或order divisibility不足；本節點尚不宣稱quotient multiplication well-defined。



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[原始題目 JSONL](https://ocme.evemisslab.com/data/questions/batches/batch-20261015-advance-20261113-r01-finite-normal-subgroup-foundations/questions.jsonl) · [驗收報告](https://ocme.evemisslab.com/data/questions/batches/batch-20261015-advance-20261113-r01-finite-normal-subgroup-foundations/validation-report.json)