# 有限群的Lagrange定理基礎 · 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-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-foundations · 2026-10-14 · 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. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-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":[0,2,4]}。請依 [subset, contains_identity, product_closed, inverse_closed, subgroup, certificate] 欄序回答。

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

Wave6第五層核對=([0, 2, 4], 是, 是, 是, 是, complete_Cayley_table_subgroup_certificate)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0001/)

有限群的Lagrange定理 · qf-mod42-lagrange-subgroup-qualification · candidate





## 2. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-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, certificate] 欄序回答。

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

Wave6第五層核對=([0, 2, 4, 6], 是, 是, 是, 是, complete_Cayley_table_subgroup_certificate)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0002/)

有限群的Lagrange定理 · qf-mod42-lagrange-subgroup-qualification · candidate





## 3. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-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":[0,2,4,6,8]}。請依 [subset, contains_identity, product_closed, inverse_closed, subgroup, certificate] 欄序回答。

查看答案與解釋([0, 2, 4, 6, 8], 是, 是, 是, 是, complete_Cayley_table_subgroup_certificate)

Wave6第五層核對=([0, 2, 4, 6, 8], 是, 是, 是, 是, complete_Cayley_table_subgroup_certificate)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0003/)

有限群的Lagrange定理 · qf-mod42-lagrange-subgroup-qualification · candidate





## 4. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-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":[0,2,4,6,8,10]}。請依 [subset, contains_identity, product_closed, inverse_closed, subgroup, certificate] 欄序回答。

查看答案與解釋([0, 2, 4, 6, 8, 10], 是, 是, 是, 是, complete_Cayley_table_subgroup_certificate)

Wave6第五層核對=([0, 2, 4, 6, 8, 10], 是, 是, 是, 是, complete_Cayley_table_subgroup_certificate)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0004/)

有限群的Lagrange定理 · qf-mod42-lagrange-subgroup-qualification · candidate





## 5. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-subgroup-qualification；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13],[1,2,3,4,5,6,7,8,9,10,11,12,13,0],[2,3,4,5,6,7,8,9,10,11,12,13,0,1],[3,4,5,6,7,8,9,10,11,12,13,0,1,2],[4,5,6,7,8,9,10,11,12,13,0,1,2,3],[5,6,7,8,9,10,11,12,13,0,1,2,3,4],[6,7,8,9,10,11,12,13,0,1,2,3,4,5],[7,8,9,10,11,12,13,0,1,2,3,4,5,6],[8,9,10,11,12,13,0,1,2,3,4,5,6,7],[9,10,11,12,13,0,1,2,3,4,5,6,7,8],[10,11,12,13,0,1,2,3,4,5,6,7,8,9],[11,12,13,0,1,2,3,4,5,6,7,8,9,10],[12,13,0,1,2,3,4,5,6,7,8,9,10,11],[13,0,1,2,3,4,5,6,7,8,9,10,11,12]],"identity":0,"subset":[0,2,4,6,8,10,12]}。請依 [subset, contains_identity, product_closed, inverse_closed, subgroup, certificate] 欄序回答。

查看答案與解釋([0, 2, 4, 6, 8, 10, 12], 是, 是, 是, 是, complete_Cayley_table_subgroup_certificate)

Wave6第五層核對=([0, 2, 4, 6, 8, 10, 12], 是, 是, 是, 是, complete_Cayley_table_subgroup_certificate)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0005/)

有限群的Lagrange定理 · qf-mod42-lagrange-subgroup-qualification · candidate





## 6. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-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":[1,3,5]}。請依 [subset, contains_identity, product_closed, inverse_closed, subgroup, certificate] 欄序回答。

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

Wave6第五層核對=([1, 3, 5], 是, 是, 是, 是, complete_Cayley_table_subgroup_certificate)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0006/)

有限群的Lagrange定理 · qf-mod42-lagrange-subgroup-qualification · candidate





## 7. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-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, certificate] 欄序回答。

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

Wave6第五層核對=([1, 3, 5, 7], 是, 是, 是, 是, complete_Cayley_table_subgroup_certificate)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0007/)

有限群的Lagrange定理 · qf-mod42-lagrange-subgroup-qualification · candidate





## 8. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-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":[1,3,5,7,9]}。請依 [subset, contains_identity, product_closed, inverse_closed, subgroup, certificate] 欄序回答。

查看答案與解釋([1, 3, 5, 7, 9], 是, 是, 是, 是, complete_Cayley_table_subgroup_certificate)

Wave6第五層核對=([1, 3, 5, 7, 9], 是, 是, 是, 是, complete_Cayley_table_subgroup_certificate)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0008/)

有限群的Lagrange定理 · qf-mod42-lagrange-subgroup-qualification · candidate





## 9. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-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":[1,3,5,7,9,11]}。請依 [subset, contains_identity, product_closed, inverse_closed, subgroup, certificate] 欄序回答。

查看答案與解釋([1, 3, 5, 7, 9, 11], 是, 是, 是, 是, complete_Cayley_table_subgroup_certificate)

Wave6第五層核對=([1, 3, 5, 7, 9, 11], 是, 是, 是, 是, complete_Cayley_table_subgroup_certificate)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0009/)

有限群的Lagrange定理 · qf-mod42-lagrange-subgroup-qualification · candidate





## 10. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-subgroup-qualification；資料={"group_table":[[13,0,1,2,3,4,5,6,7,8,9,10,11,12],[0,1,2,3,4,5,6,7,8,9,10,11,12,13],[1,2,3,4,5,6,7,8,9,10,11,12,13,0],[2,3,4,5,6,7,8,9,10,11,12,13,0,1],[3,4,5,6,7,8,9,10,11,12,13,0,1,2],[4,5,6,7,8,9,10,11,12,13,0,1,2,3],[5,6,7,8,9,10,11,12,13,0,1,2,3,4],[6,7,8,9,10,11,12,13,0,1,2,3,4,5],[7,8,9,10,11,12,13,0,1,2,3,4,5,6],[8,9,10,11,12,13,0,1,2,3,4,5,6,7],[9,10,11,12,13,0,1,2,3,4,5,6,7,8],[10,11,12,13,0,1,2,3,4,5,6,7,8,9],[11,12,13,0,1,2,3,4,5,6,7,8,9,10],[12,13,0,1,2,3,4,5,6,7,8,9,10,11]],"identity":1,"subset":[1,3,5,7,9,11,13]}。請依 [subset, contains_identity, product_closed, inverse_closed, subgroup, certificate] 欄序回答。

查看答案與解釋([1, 3, 5, 7, 9, 11, 13], 是, 是, 是, 是, complete_Cayley_table_subgroup_certificate)

Wave6第五層核對=([1, 3, 5, 7, 9, 11, 13], 是, 是, 是, 是, complete_Cayley_table_subgroup_certificate)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0010/)

有限群的Lagrange定理 · qf-mod42-lagrange-subgroup-qualification · candidate





## 11. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-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":[0,2,4]}。請依 [subset, contains_identity, product_closed, inverse_closed, subgroup, certificate] 欄序回答。

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

Wave6第五層核對=([0, 2, 4], 是, 是, 是, 是, complete_Cayley_table_subgroup_certificate)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0011/)

有限群的Lagrange定理 · qf-mod42-lagrange-subgroup-qualification · candidate





## 12. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-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, certificate] 欄序回答。

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

Wave6第五層核對=([0, 2, 4, 6], 是, 是, 是, 是, complete_Cayley_table_subgroup_certificate)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0012/)

有限群的Lagrange定理 · qf-mod42-lagrange-subgroup-qualification · candidate





## 13. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-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":[0,2,4,6,8]}。請依 [subset, contains_identity, product_closed, inverse_closed, subgroup, certificate] 欄序回答。

查看答案與解釋([0, 2, 4, 6, 8], 是, 是, 是, 是, complete_Cayley_table_subgroup_certificate)

Wave6第五層核對=([0, 2, 4, 6, 8], 是, 是, 是, 是, complete_Cayley_table_subgroup_certificate)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0013/)

有限群的Lagrange定理 · qf-mod42-lagrange-subgroup-qualification · candidate





## 14. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-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":[0,2,4,6,8,10]}。請依 [subset, contains_identity, product_closed, inverse_closed, subgroup, certificate] 欄序回答。

查看答案與解釋([0, 2, 4, 6, 8, 10], 是, 是, 是, 是, complete_Cayley_table_subgroup_certificate)

Wave6第五層核對=([0, 2, 4, 6, 8, 10], 是, 是, 是, 是, complete_Cayley_table_subgroup_certificate)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0014/)

有限群的Lagrange定理 · qf-mod42-lagrange-subgroup-qualification · candidate





## 15. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-subgroup-qualification；資料={"group_table":[[12,13,0,1,2,3,4,5,6,7,8,9,10,11],[13,0,1,2,3,4,5,6,7,8,9,10,11,12],[0,1,2,3,4,5,6,7,8,9,10,11,12,13],[1,2,3,4,5,6,7,8,9,10,11,12,13,0],[2,3,4,5,6,7,8,9,10,11,12,13,0,1],[3,4,5,6,7,8,9,10,11,12,13,0,1,2],[4,5,6,7,8,9,10,11,12,13,0,1,2,3],[5,6,7,8,9,10,11,12,13,0,1,2,3,4],[6,7,8,9,10,11,12,13,0,1,2,3,4,5],[7,8,9,10,11,12,13,0,1,2,3,4,5,6],[8,9,10,11,12,13,0,1,2,3,4,5,6,7],[9,10,11,12,13,0,1,2,3,4,5,6,7,8],[10,11,12,13,0,1,2,3,4,5,6,7,8,9],[11,12,13,0,1,2,3,4,5,6,7,8,9,10]],"identity":2,"subset":[0,2,4,6,8,10,12]}。請依 [subset, contains_identity, product_closed, inverse_closed, subgroup, certificate] 欄序回答。

查看答案與解釋([0, 2, 4, 6, 8, 10, 12], 是, 是, 是, 是, complete_Cayley_table_subgroup_certificate)

Wave6第五層核對=([0, 2, 4, 6, 8, 10, 12], 是, 是, 是, 是, complete_Cayley_table_subgroup_certificate)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0015/)

有限群的Lagrange定理 · qf-mod42-lagrange-subgroup-qualification · candidate





## 16. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-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":[1,3,5]}。請依 [subset, contains_identity, product_closed, inverse_closed, subgroup, certificate] 欄序回答。

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

Wave6第五層核對=([1, 3, 5], 是, 是, 是, 是, complete_Cayley_table_subgroup_certificate)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0016/)

有限群的Lagrange定理 · qf-mod42-lagrange-subgroup-qualification · candidate





## 17. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-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, certificate] 欄序回答。

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

Wave6第五層核對=([1, 3, 5, 7], 是, 是, 是, 是, complete_Cayley_table_subgroup_certificate)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0017/)

有限群的Lagrange定理 · qf-mod42-lagrange-subgroup-qualification · candidate





## 18. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-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":[1,3,5,7,9]}。請依 [subset, contains_identity, product_closed, inverse_closed, subgroup, certificate] 欄序回答。

查看答案與解釋([1, 3, 5, 7, 9], 是, 是, 是, 是, complete_Cayley_table_subgroup_certificate)

Wave6第五層核對=([1, 3, 5, 7, 9], 是, 是, 是, 是, complete_Cayley_table_subgroup_certificate)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0018/)

有限群的Lagrange定理 · qf-mod42-lagrange-subgroup-qualification · candidate





## 19. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-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":[1,3,5,7,9,11]}。請依 [subset, contains_identity, product_closed, inverse_closed, subgroup, certificate] 欄序回答。

查看答案與解釋([1, 3, 5, 7, 9, 11], 是, 是, 是, 是, complete_Cayley_table_subgroup_certificate)

Wave6第五層核對=([1, 3, 5, 7, 9, 11], 是, 是, 是, 是, complete_Cayley_table_subgroup_certificate)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0019/)

有限群的Lagrange定理 · qf-mod42-lagrange-subgroup-qualification · candidate





## 20. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-subgroup-qualification；資料={"group_table":[[11,12,13,0,1,2,3,4,5,6,7,8,9,10],[12,13,0,1,2,3,4,5,6,7,8,9,10,11],[13,0,1,2,3,4,5,6,7,8,9,10,11,12],[0,1,2,3,4,5,6,7,8,9,10,11,12,13],[1,2,3,4,5,6,7,8,9,10,11,12,13,0],[2,3,4,5,6,7,8,9,10,11,12,13,0,1],[3,4,5,6,7,8,9,10,11,12,13,0,1,2],[4,5,6,7,8,9,10,11,12,13,0,1,2,3],[5,6,7,8,9,10,11,12,13,0,1,2,3,4],[6,7,8,9,10,11,12,13,0,1,2,3,4,5],[7,8,9,10,11,12,13,0,1,2,3,4,5,6],[8,9,10,11,12,13,0,1,2,3,4,5,6,7],[9,10,11,12,13,0,1,2,3,4,5,6,7,8],[10,11,12,13,0,1,2,3,4,5,6,7,8,9]],"identity":3,"subset":[1,3,5,7,9,11,13]}。請依 [subset, contains_identity, product_closed, inverse_closed, subgroup, certificate] 欄序回答。

查看答案與解釋([1, 3, 5, 7, 9, 11, 13], 是, 是, 是, 是, complete_Cayley_table_subgroup_certificate)

Wave6第五層核對=([1, 3, 5, 7, 9, 11, 13], 是, 是, 是, 是, complete_Cayley_table_subgroup_certificate)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0020/)

有限群的Lagrange定理 · qf-mod42-lagrange-subgroup-qualification · candidate





## 21. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-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":[0,2,4]}。請依 [subset, contains_identity, product_closed, inverse_closed, subgroup, certificate] 欄序回答。

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

Wave6第五層核對=([0, 2, 4], 是, 是, 是, 是, complete_Cayley_table_subgroup_certificate)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0021/)

有限群的Lagrange定理 · qf-mod42-lagrange-subgroup-qualification · candidate





## 22. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-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, certificate] 欄序回答。

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

Wave6第五層核對=([0, 2, 4, 6], 是, 是, 是, 是, complete_Cayley_table_subgroup_certificate)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0022/)

有限群的Lagrange定理 · qf-mod42-lagrange-subgroup-qualification · candidate





## 23. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-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":[0,2,4,6,8]}。請依 [subset, contains_identity, product_closed, inverse_closed, subgroup, certificate] 欄序回答。

查看答案與解釋([0, 2, 4, 6, 8], 是, 是, 是, 是, complete_Cayley_table_subgroup_certificate)

Wave6第五層核對=([0, 2, 4, 6, 8], 是, 是, 是, 是, complete_Cayley_table_subgroup_certificate)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0023/)

有限群的Lagrange定理 · qf-mod42-lagrange-subgroup-qualification · candidate





## 24. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-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":[0,2,4,6,8,10]}。請依 [subset, contains_identity, product_closed, inverse_closed, subgroup, certificate] 欄序回答。

查看答案與解釋([0, 2, 4, 6, 8, 10], 是, 是, 是, 是, complete_Cayley_table_subgroup_certificate)

Wave6第五層核對=([0, 2, 4, 6, 8, 10], 是, 是, 是, 是, complete_Cayley_table_subgroup_certificate)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0024/)

有限群的Lagrange定理 · qf-mod42-lagrange-subgroup-qualification · candidate





## 25. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-subgroup-qualification；資料={"group_table":[[10,11,12,13,0,1,2,3,4,5,6,7,8,9],[11,12,13,0,1,2,3,4,5,6,7,8,9,10],[12,13,0,1,2,3,4,5,6,7,8,9,10,11],[13,0,1,2,3,4,5,6,7,8,9,10,11,12],[0,1,2,3,4,5,6,7,8,9,10,11,12,13],[1,2,3,4,5,6,7,8,9,10,11,12,13,0],[2,3,4,5,6,7,8,9,10,11,12,13,0,1],[3,4,5,6,7,8,9,10,11,12,13,0,1,2],[4,5,6,7,8,9,10,11,12,13,0,1,2,3],[5,6,7,8,9,10,11,12,13,0,1,2,3,4],[6,7,8,9,10,11,12,13,0,1,2,3,4,5],[7,8,9,10,11,12,13,0,1,2,3,4,5,6],[8,9,10,11,12,13,0,1,2,3,4,5,6,7],[9,10,11,12,13,0,1,2,3,4,5,6,7,8]],"identity":4,"subset":[0,2,4,6,8,10,12]}。請依 [subset, contains_identity, product_closed, inverse_closed, subgroup, certificate] 欄序回答。

查看答案與解釋([0, 2, 4, 6, 8, 10, 12], 是, 是, 是, 是, complete_Cayley_table_subgroup_certificate)

Wave6第五層核對=([0, 2, 4, 6, 8, 10, 12], 是, 是, 是, 是, complete_Cayley_table_subgroup_certificate)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0025/)

有限群的Lagrange定理 · qf-mod42-lagrange-subgroup-qualification · candidate





## 26. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-left-coset-partition；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":[0,2,4]}。請依 [representative_coset_rows, equal_sizes, flattened_elements, partition_certificate, certificate] 欄序回答。

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

Wave6第五層核對=([[0, [0, 2, 4]], [1, [1, 3, 5]]], 是, [0, 1, 2, 3, 4, 5], 是, left_cosets_equal_or_disjoint_and_cover_G)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0026/)

有限群的Lagrange定理 · qf-mod42-lagrange-left-coset-partition · candidate





## 27. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-left-coset-partition；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 [representative_coset_rows, equal_sizes, flattened_elements, partition_certificate, certificate] 欄序回答。

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

Wave6第五層核對=([[0, [0, 2, 4, 6]], [1, [1, 3, 5, 7]]], 是, [0, 1, 2, 3, 4, 5, 6, 7], 是, left_cosets_equal_or_disjoint_and_cover_G)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0027/)

有限群的Lagrange定理 · qf-mod42-lagrange-left-coset-partition · candidate





## 28. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-left-coset-partition；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":[0,2,4,6,8]}。請依 [representative_coset_rows, equal_sizes, flattened_elements, partition_certificate, certificate] 欄序回答。

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

Wave6第五層核對=([[0, [0, 2, 4, 6, 8]], [1, [1, 3, 5, 7, 9]]], 是, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是, left_cosets_equal_or_disjoint_and_cover_G)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0028/)

有限群的Lagrange定理 · qf-mod42-lagrange-left-coset-partition · candidate





## 29. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-left-coset-partition；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":[0,2,4,6,8,10]}。請依 [representative_coset_rows, equal_sizes, flattened_elements, partition_certificate, certificate] 欄序回答。

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

Wave6第五層核對=([[0, [0, 2, 4, 6, 8, 10]], [1, [1, 3, 5, 7, 9, 11]]], 是, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是, left_cosets_equal_or_disjoint_and_cover_G)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0029/)

有限群的Lagrange定理 · qf-mod42-lagrange-left-coset-partition · candidate





## 30. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-left-coset-partition；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13],[1,2,3,4,5,6,7,8,9,10,11,12,13,0],[2,3,4,5,6,7,8,9,10,11,12,13,0,1],[3,4,5,6,7,8,9,10,11,12,13,0,1,2],[4,5,6,7,8,9,10,11,12,13,0,1,2,3],[5,6,7,8,9,10,11,12,13,0,1,2,3,4],[6,7,8,9,10,11,12,13,0,1,2,3,4,5],[7,8,9,10,11,12,13,0,1,2,3,4,5,6],[8,9,10,11,12,13,0,1,2,3,4,5,6,7],[9,10,11,12,13,0,1,2,3,4,5,6,7,8],[10,11,12,13,0,1,2,3,4,5,6,7,8,9],[11,12,13,0,1,2,3,4,5,6,7,8,9,10],[12,13,0,1,2,3,4,5,6,7,8,9,10,11],[13,0,1,2,3,4,5,6,7,8,9,10,11,12]],"identity":0,"subset":[0,2,4,6,8,10,12]}。請依 [representative_coset_rows, equal_sizes, flattened_elements, partition_certificate, certificate] 欄序回答。

查看答案與解釋([[0, [0, 2, 4, 6, 8, 10, 12]], [1, [1, 3, 5, 7, 9, 11, 13]]], 是, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13], 是, left_cosets_equal_or_disjoint_and_cover_G)

Wave6第五層核對=([[0, [0, 2, 4, 6, 8, 10, 12]], [1, [1, 3, 5, 7, 9, 11, 13]]], 是, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13], 是, left_cosets_equal_or_disjoint_and_cover_G)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0030/)

有限群的Lagrange定理 · qf-mod42-lagrange-left-coset-partition · candidate





## 31. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-left-coset-partition；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":[1,3,5]}。請依 [representative_coset_rows, equal_sizes, flattened_elements, partition_certificate, certificate] 欄序回答。

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

Wave6第五層核對=([[0, [0, 2, 4]], [1, [1, 3, 5]]], 是, [0, 1, 2, 3, 4, 5], 是, left_cosets_equal_or_disjoint_and_cover_G)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0031/)

有限群的Lagrange定理 · qf-mod42-lagrange-left-coset-partition · candidate





## 32. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-left-coset-partition；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 [representative_coset_rows, equal_sizes, flattened_elements, partition_certificate, certificate] 欄序回答。

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

Wave6第五層核對=([[0, [0, 2, 4, 6]], [1, [1, 3, 5, 7]]], 是, [0, 1, 2, 3, 4, 5, 6, 7], 是, left_cosets_equal_or_disjoint_and_cover_G)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0032/)

有限群的Lagrange定理 · qf-mod42-lagrange-left-coset-partition · candidate





## 33. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-left-coset-partition；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":[1,3,5,7,9]}。請依 [representative_coset_rows, equal_sizes, flattened_elements, partition_certificate, certificate] 欄序回答。

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

Wave6第五層核對=([[0, [0, 2, 4, 6, 8]], [1, [1, 3, 5, 7, 9]]], 是, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是, left_cosets_equal_or_disjoint_and_cover_G)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0033/)

有限群的Lagrange定理 · qf-mod42-lagrange-left-coset-partition · candidate





## 34. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-left-coset-partition；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":[1,3,5,7,9,11]}。請依 [representative_coset_rows, equal_sizes, flattened_elements, partition_certificate, certificate] 欄序回答。

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

Wave6第五層核對=([[0, [0, 2, 4, 6, 8, 10]], [1, [1, 3, 5, 7, 9, 11]]], 是, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是, left_cosets_equal_or_disjoint_and_cover_G)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0034/)

有限群的Lagrange定理 · qf-mod42-lagrange-left-coset-partition · candidate





## 35. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-left-coset-partition；資料={"group_table":[[13,0,1,2,3,4,5,6,7,8,9,10,11,12],[0,1,2,3,4,5,6,7,8,9,10,11,12,13],[1,2,3,4,5,6,7,8,9,10,11,12,13,0],[2,3,4,5,6,7,8,9,10,11,12,13,0,1],[3,4,5,6,7,8,9,10,11,12,13,0,1,2],[4,5,6,7,8,9,10,11,12,13,0,1,2,3],[5,6,7,8,9,10,11,12,13,0,1,2,3,4],[6,7,8,9,10,11,12,13,0,1,2,3,4,5],[7,8,9,10,11,12,13,0,1,2,3,4,5,6],[8,9,10,11,12,13,0,1,2,3,4,5,6,7],[9,10,11,12,13,0,1,2,3,4,5,6,7,8],[10,11,12,13,0,1,2,3,4,5,6,7,8,9],[11,12,13,0,1,2,3,4,5,6,7,8,9,10],[12,13,0,1,2,3,4,5,6,7,8,9,10,11]],"identity":1,"subset":[1,3,5,7,9,11,13]}。請依 [representative_coset_rows, equal_sizes, flattened_elements, partition_certificate, certificate] 欄序回答。

查看答案與解釋([[0, [0, 2, 4, 6, 8, 10, 12]], [1, [1, 3, 5, 7, 9, 11, 13]]], 是, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13], 是, left_cosets_equal_or_disjoint_and_cover_G)

Wave6第五層核對=([[0, [0, 2, 4, 6, 8, 10, 12]], [1, [1, 3, 5, 7, 9, 11, 13]]], 是, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13], 是, left_cosets_equal_or_disjoint_and_cover_G)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0035/)

有限群的Lagrange定理 · qf-mod42-lagrange-left-coset-partition · candidate





## 36. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-left-coset-partition；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":[0,2,4]}。請依 [representative_coset_rows, equal_sizes, flattened_elements, partition_certificate, certificate] 欄序回答。

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

Wave6第五層核對=([[0, [0, 2, 4]], [1, [1, 3, 5]]], 是, [0, 1, 2, 3, 4, 5], 是, left_cosets_equal_or_disjoint_and_cover_G)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0036/)

有限群的Lagrange定理 · qf-mod42-lagrange-left-coset-partition · candidate





## 37. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-left-coset-partition；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 [representative_coset_rows, equal_sizes, flattened_elements, partition_certificate, certificate] 欄序回答。

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

Wave6第五層核對=([[0, [0, 2, 4, 6]], [1, [1, 3, 5, 7]]], 是, [0, 1, 2, 3, 4, 5, 6, 7], 是, left_cosets_equal_or_disjoint_and_cover_G)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0037/)

有限群的Lagrange定理 · qf-mod42-lagrange-left-coset-partition · candidate





## 38. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-left-coset-partition；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":[0,2,4,6,8]}。請依 [representative_coset_rows, equal_sizes, flattened_elements, partition_certificate, certificate] 欄序回答。

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

Wave6第五層核對=([[0, [0, 2, 4, 6, 8]], [1, [1, 3, 5, 7, 9]]], 是, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是, left_cosets_equal_or_disjoint_and_cover_G)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0038/)

有限群的Lagrange定理 · qf-mod42-lagrange-left-coset-partition · candidate





## 39. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-left-coset-partition；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":[0,2,4,6,8,10]}。請依 [representative_coset_rows, equal_sizes, flattened_elements, partition_certificate, certificate] 欄序回答。

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

Wave6第五層核對=([[0, [0, 2, 4, 6, 8, 10]], [1, [1, 3, 5, 7, 9, 11]]], 是, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是, left_cosets_equal_or_disjoint_and_cover_G)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0039/)

有限群的Lagrange定理 · qf-mod42-lagrange-left-coset-partition · candidate





## 40. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-left-coset-partition；資料={"group_table":[[12,13,0,1,2,3,4,5,6,7,8,9,10,11],[13,0,1,2,3,4,5,6,7,8,9,10,11,12],[0,1,2,3,4,5,6,7,8,9,10,11,12,13],[1,2,3,4,5,6,7,8,9,10,11,12,13,0],[2,3,4,5,6,7,8,9,10,11,12,13,0,1],[3,4,5,6,7,8,9,10,11,12,13,0,1,2],[4,5,6,7,8,9,10,11,12,13,0,1,2,3],[5,6,7,8,9,10,11,12,13,0,1,2,3,4],[6,7,8,9,10,11,12,13,0,1,2,3,4,5],[7,8,9,10,11,12,13,0,1,2,3,4,5,6],[8,9,10,11,12,13,0,1,2,3,4,5,6,7],[9,10,11,12,13,0,1,2,3,4,5,6,7,8],[10,11,12,13,0,1,2,3,4,5,6,7,8,9],[11,12,13,0,1,2,3,4,5,6,7,8,9,10]],"identity":2,"subset":[0,2,4,6,8,10,12]}。請依 [representative_coset_rows, equal_sizes, flattened_elements, partition_certificate, certificate] 欄序回答。

查看答案與解釋([[0, [0, 2, 4, 6, 8, 10, 12]], [1, [1, 3, 5, 7, 9, 11, 13]]], 是, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13], 是, left_cosets_equal_or_disjoint_and_cover_G)

Wave6第五層核對=([[0, [0, 2, 4, 6, 8, 10, 12]], [1, [1, 3, 5, 7, 9, 11, 13]]], 是, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13], 是, left_cosets_equal_or_disjoint_and_cover_G)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0040/)

有限群的Lagrange定理 · qf-mod42-lagrange-left-coset-partition · candidate





## 41. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-left-coset-partition；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":[1,3,5]}。請依 [representative_coset_rows, equal_sizes, flattened_elements, partition_certificate, certificate] 欄序回答。

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

Wave6第五層核對=([[0, [0, 2, 4]], [1, [1, 3, 5]]], 是, [0, 1, 2, 3, 4, 5], 是, left_cosets_equal_or_disjoint_and_cover_G)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0041/)

有限群的Lagrange定理 · qf-mod42-lagrange-left-coset-partition · candidate





## 42. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-left-coset-partition；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 [representative_coset_rows, equal_sizes, flattened_elements, partition_certificate, certificate] 欄序回答。

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

Wave6第五層核對=([[0, [0, 2, 4, 6]], [1, [1, 3, 5, 7]]], 是, [0, 1, 2, 3, 4, 5, 6, 7], 是, left_cosets_equal_or_disjoint_and_cover_G)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0042/)

有限群的Lagrange定理 · qf-mod42-lagrange-left-coset-partition · candidate





## 43. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-left-coset-partition；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":[1,3,5,7,9]}。請依 [representative_coset_rows, equal_sizes, flattened_elements, partition_certificate, certificate] 欄序回答。

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

Wave6第五層核對=([[0, [0, 2, 4, 6, 8]], [1, [1, 3, 5, 7, 9]]], 是, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是, left_cosets_equal_or_disjoint_and_cover_G)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0043/)

有限群的Lagrange定理 · qf-mod42-lagrange-left-coset-partition · candidate





## 44. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-left-coset-partition；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":[1,3,5,7,9,11]}。請依 [representative_coset_rows, equal_sizes, flattened_elements, partition_certificate, certificate] 欄序回答。

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

Wave6第五層核對=([[0, [0, 2, 4, 6, 8, 10]], [1, [1, 3, 5, 7, 9, 11]]], 是, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是, left_cosets_equal_or_disjoint_and_cover_G)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0044/)

有限群的Lagrange定理 · qf-mod42-lagrange-left-coset-partition · candidate





## 45. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-left-coset-partition；資料={"group_table":[[11,12,13,0,1,2,3,4,5,6,7,8,9,10],[12,13,0,1,2,3,4,5,6,7,8,9,10,11],[13,0,1,2,3,4,5,6,7,8,9,10,11,12],[0,1,2,3,4,5,6,7,8,9,10,11,12,13],[1,2,3,4,5,6,7,8,9,10,11,12,13,0],[2,3,4,5,6,7,8,9,10,11,12,13,0,1],[3,4,5,6,7,8,9,10,11,12,13,0,1,2],[4,5,6,7,8,9,10,11,12,13,0,1,2,3],[5,6,7,8,9,10,11,12,13,0,1,2,3,4],[6,7,8,9,10,11,12,13,0,1,2,3,4,5],[7,8,9,10,11,12,13,0,1,2,3,4,5,6],[8,9,10,11,12,13,0,1,2,3,4,5,6,7],[9,10,11,12,13,0,1,2,3,4,5,6,7,8],[10,11,12,13,0,1,2,3,4,5,6,7,8,9]],"identity":3,"subset":[1,3,5,7,9,11,13]}。請依 [representative_coset_rows, equal_sizes, flattened_elements, partition_certificate, certificate] 欄序回答。

查看答案與解釋([[0, [0, 2, 4, 6, 8, 10, 12]], [1, [1, 3, 5, 7, 9, 11, 13]]], 是, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13], 是, left_cosets_equal_or_disjoint_and_cover_G)

Wave6第五層核對=([[0, [0, 2, 4, 6, 8, 10, 12]], [1, [1, 3, 5, 7, 9, 11, 13]]], 是, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13], 是, left_cosets_equal_or_disjoint_and_cover_G)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0045/)

有限群的Lagrange定理 · qf-mod42-lagrange-left-coset-partition · candidate





## 46. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-left-coset-partition；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":[0,2,4]}。請依 [representative_coset_rows, equal_sizes, flattened_elements, partition_certificate, certificate] 欄序回答。

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

Wave6第五層核對=([[0, [0, 2, 4]], [1, [1, 3, 5]]], 是, [0, 1, 2, 3, 4, 5], 是, left_cosets_equal_or_disjoint_and_cover_G)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0046/)

有限群的Lagrange定理 · qf-mod42-lagrange-left-coset-partition · candidate





## 47. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-left-coset-partition；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 [representative_coset_rows, equal_sizes, flattened_elements, partition_certificate, certificate] 欄序回答。

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

Wave6第五層核對=([[0, [0, 2, 4, 6]], [1, [1, 3, 5, 7]]], 是, [0, 1, 2, 3, 4, 5, 6, 7], 是, left_cosets_equal_or_disjoint_and_cover_G)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0047/)

有限群的Lagrange定理 · qf-mod42-lagrange-left-coset-partition · candidate





## 48. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-left-coset-partition；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":[0,2,4,6,8]}。請依 [representative_coset_rows, equal_sizes, flattened_elements, partition_certificate, certificate] 欄序回答。

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

Wave6第五層核對=([[0, [0, 2, 4, 6, 8]], [1, [1, 3, 5, 7, 9]]], 是, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是, left_cosets_equal_or_disjoint_and_cover_G)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0048/)

有限群的Lagrange定理 · qf-mod42-lagrange-left-coset-partition · candidate





## 49. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-left-coset-partition；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":[0,2,4,6,8,10]}。請依 [representative_coset_rows, equal_sizes, flattened_elements, partition_certificate, certificate] 欄序回答。

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

Wave6第五層核對=([[0, [0, 2, 4, 6, 8, 10]], [1, [1, 3, 5, 7, 9, 11]]], 是, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是, left_cosets_equal_or_disjoint_and_cover_G)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0049/)

有限群的Lagrange定理 · qf-mod42-lagrange-left-coset-partition · candidate





## 50. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-left-coset-partition；資料={"group_table":[[10,11,12,13,0,1,2,3,4,5,6,7,8,9],[11,12,13,0,1,2,3,4,5,6,7,8,9,10],[12,13,0,1,2,3,4,5,6,7,8,9,10,11],[13,0,1,2,3,4,5,6,7,8,9,10,11,12],[0,1,2,3,4,5,6,7,8,9,10,11,12,13],[1,2,3,4,5,6,7,8,9,10,11,12,13,0],[2,3,4,5,6,7,8,9,10,11,12,13,0,1],[3,4,5,6,7,8,9,10,11,12,13,0,1,2],[4,5,6,7,8,9,10,11,12,13,0,1,2,3],[5,6,7,8,9,10,11,12,13,0,1,2,3,4],[6,7,8,9,10,11,12,13,0,1,2,3,4,5],[7,8,9,10,11,12,13,0,1,2,3,4,5,6],[8,9,10,11,12,13,0,1,2,3,4,5,6,7],[9,10,11,12,13,0,1,2,3,4,5,6,7,8]],"identity":4,"subset":[0,2,4,6,8,10,12]}。請依 [representative_coset_rows, equal_sizes, flattened_elements, partition_certificate, certificate] 欄序回答。

查看答案與解釋([[0, [0, 2, 4, 6, 8, 10, 12]], [1, [1, 3, 5, 7, 9, 11, 13]]], 是, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13], 是, left_cosets_equal_or_disjoint_and_cover_G)

Wave6第五層核對=([[0, [0, 2, 4, 6, 8, 10, 12]], [1, [1, 3, 5, 7, 9, 11, 13]]], 是, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13], 是, left_cosets_equal_or_disjoint_and_cover_G)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0050/)

有限群的Lagrange定理 · qf-mod42-lagrange-left-coset-partition · candidate





## 51. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-divisibility-identity；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":[0,2,4]}。請依 [group_order, subgroup_order, index, product, remainder, equal] 欄序回答。

查看答案與解釋(6, 3, 2, 6, 0, 是)

Wave6第五層核對=(6, 3, 2, 6, 0, 是)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0051/)

有限群的Lagrange定理 · qf-mod42-lagrange-divisibility-identity · candidate





## 52. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-divisibility-identity；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 [group_order, subgroup_order, index, product, remainder, equal] 欄序回答。

查看答案與解釋(8, 4, 2, 8, 0, 是)

Wave6第五層核對=(8, 4, 2, 8, 0, 是)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0052/)

有限群的Lagrange定理 · qf-mod42-lagrange-divisibility-identity · candidate





## 53. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-divisibility-identity；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":[0,2,4,6,8]}。請依 [group_order, subgroup_order, index, product, remainder, equal] 欄序回答。

查看答案與解釋(10, 5, 2, 10, 0, 是)

Wave6第五層核對=(10, 5, 2, 10, 0, 是)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0053/)

有限群的Lagrange定理 · qf-mod42-lagrange-divisibility-identity · candidate





## 54. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-divisibility-identity；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":[0,2,4,6,8,10]}。請依 [group_order, subgroup_order, index, product, remainder, equal] 欄序回答。

查看答案與解釋(12, 6, 2, 12, 0, 是)

Wave6第五層核對=(12, 6, 2, 12, 0, 是)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0054/)

有限群的Lagrange定理 · qf-mod42-lagrange-divisibility-identity · candidate





## 55. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-divisibility-identity；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13],[1,2,3,4,5,6,7,8,9,10,11,12,13,0],[2,3,4,5,6,7,8,9,10,11,12,13,0,1],[3,4,5,6,7,8,9,10,11,12,13,0,1,2],[4,5,6,7,8,9,10,11,12,13,0,1,2,3],[5,6,7,8,9,10,11,12,13,0,1,2,3,4],[6,7,8,9,10,11,12,13,0,1,2,3,4,5],[7,8,9,10,11,12,13,0,1,2,3,4,5,6],[8,9,10,11,12,13,0,1,2,3,4,5,6,7],[9,10,11,12,13,0,1,2,3,4,5,6,7,8],[10,11,12,13,0,1,2,3,4,5,6,7,8,9],[11,12,13,0,1,2,3,4,5,6,7,8,9,10],[12,13,0,1,2,3,4,5,6,7,8,9,10,11],[13,0,1,2,3,4,5,6,7,8,9,10,11,12]],"identity":0,"subset":[0,2,4,6,8,10,12]}。請依 [group_order, subgroup_order, index, product, remainder, equal] 欄序回答。

查看答案與解釋(14, 7, 2, 14, 0, 是)

Wave6第五層核對=(14, 7, 2, 14, 0, 是)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0055/)

有限群的Lagrange定理 · qf-mod42-lagrange-divisibility-identity · candidate





## 56. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-divisibility-identity；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":[1,3,5]}。請依 [group_order, subgroup_order, index, product, remainder, equal] 欄序回答。

查看答案與解釋(6, 3, 2, 6, 0, 是)

Wave6第五層核對=(6, 3, 2, 6, 0, 是)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0056/)

有限群的Lagrange定理 · qf-mod42-lagrange-divisibility-identity · candidate





## 57. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-divisibility-identity；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 [group_order, subgroup_order, index, product, remainder, equal] 欄序回答。

查看答案與解釋(8, 4, 2, 8, 0, 是)

Wave6第五層核對=(8, 4, 2, 8, 0, 是)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0057/)

有限群的Lagrange定理 · qf-mod42-lagrange-divisibility-identity · candidate





## 58. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-divisibility-identity；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":[1,3,5,7,9]}。請依 [group_order, subgroup_order, index, product, remainder, equal] 欄序回答。

查看答案與解釋(10, 5, 2, 10, 0, 是)

Wave6第五層核對=(10, 5, 2, 10, 0, 是)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0058/)

有限群的Lagrange定理 · qf-mod42-lagrange-divisibility-identity · candidate





## 59. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-divisibility-identity；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":[1,3,5,7,9,11]}。請依 [group_order, subgroup_order, index, product, remainder, equal] 欄序回答。

查看答案與解釋(12, 6, 2, 12, 0, 是)

Wave6第五層核對=(12, 6, 2, 12, 0, 是)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0059/)

有限群的Lagrange定理 · qf-mod42-lagrange-divisibility-identity · candidate





## 60. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-divisibility-identity；資料={"group_table":[[13,0,1,2,3,4,5,6,7,8,9,10,11,12],[0,1,2,3,4,5,6,7,8,9,10,11,12,13],[1,2,3,4,5,6,7,8,9,10,11,12,13,0],[2,3,4,5,6,7,8,9,10,11,12,13,0,1],[3,4,5,6,7,8,9,10,11,12,13,0,1,2],[4,5,6,7,8,9,10,11,12,13,0,1,2,3],[5,6,7,8,9,10,11,12,13,0,1,2,3,4],[6,7,8,9,10,11,12,13,0,1,2,3,4,5],[7,8,9,10,11,12,13,0,1,2,3,4,5,6],[8,9,10,11,12,13,0,1,2,3,4,5,6,7],[9,10,11,12,13,0,1,2,3,4,5,6,7,8],[10,11,12,13,0,1,2,3,4,5,6,7,8,9],[11,12,13,0,1,2,3,4,5,6,7,8,9,10],[12,13,0,1,2,3,4,5,6,7,8,9,10,11]],"identity":1,"subset":[1,3,5,7,9,11,13]}。請依 [group_order, subgroup_order, index, product, remainder, equal] 欄序回答。

查看答案與解釋(14, 7, 2, 14, 0, 是)

Wave6第五層核對=(14, 7, 2, 14, 0, 是)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0060/)

有限群的Lagrange定理 · qf-mod42-lagrange-divisibility-identity · candidate





## 61. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-divisibility-identity；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":[0,2,4]}。請依 [group_order, subgroup_order, index, product, remainder, equal] 欄序回答。

查看答案與解釋(6, 3, 2, 6, 0, 是)

Wave6第五層核對=(6, 3, 2, 6, 0, 是)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0061/)

有限群的Lagrange定理 · qf-mod42-lagrange-divisibility-identity · candidate





## 62. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-divisibility-identity；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 [group_order, subgroup_order, index, product, remainder, equal] 欄序回答。

查看答案與解釋(8, 4, 2, 8, 0, 是)

Wave6第五層核對=(8, 4, 2, 8, 0, 是)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0062/)

有限群的Lagrange定理 · qf-mod42-lagrange-divisibility-identity · candidate





## 63. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-divisibility-identity；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":[0,2,4,6,8]}。請依 [group_order, subgroup_order, index, product, remainder, equal] 欄序回答。

查看答案與解釋(10, 5, 2, 10, 0, 是)

Wave6第五層核對=(10, 5, 2, 10, 0, 是)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0063/)

有限群的Lagrange定理 · qf-mod42-lagrange-divisibility-identity · candidate





## 64. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-divisibility-identity；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":[0,2,4,6,8,10]}。請依 [group_order, subgroup_order, index, product, remainder, equal] 欄序回答。

查看答案與解釋(12, 6, 2, 12, 0, 是)

Wave6第五層核對=(12, 6, 2, 12, 0, 是)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0064/)

有限群的Lagrange定理 · qf-mod42-lagrange-divisibility-identity · candidate





## 65. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-divisibility-identity；資料={"group_table":[[12,13,0,1,2,3,4,5,6,7,8,9,10,11],[13,0,1,2,3,4,5,6,7,8,9,10,11,12],[0,1,2,3,4,5,6,7,8,9,10,11,12,13],[1,2,3,4,5,6,7,8,9,10,11,12,13,0],[2,3,4,5,6,7,8,9,10,11,12,13,0,1],[3,4,5,6,7,8,9,10,11,12,13,0,1,2],[4,5,6,7,8,9,10,11,12,13,0,1,2,3],[5,6,7,8,9,10,11,12,13,0,1,2,3,4],[6,7,8,9,10,11,12,13,0,1,2,3,4,5],[7,8,9,10,11,12,13,0,1,2,3,4,5,6],[8,9,10,11,12,13,0,1,2,3,4,5,6,7],[9,10,11,12,13,0,1,2,3,4,5,6,7,8],[10,11,12,13,0,1,2,3,4,5,6,7,8,9],[11,12,13,0,1,2,3,4,5,6,7,8,9,10]],"identity":2,"subset":[0,2,4,6,8,10,12]}。請依 [group_order, subgroup_order, index, product, remainder, equal] 欄序回答。

查看答案與解釋(14, 7, 2, 14, 0, 是)

Wave6第五層核對=(14, 7, 2, 14, 0, 是)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0065/)

有限群的Lagrange定理 · qf-mod42-lagrange-divisibility-identity · candidate





## 66. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-divisibility-identity；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":[1,3,5]}。請依 [group_order, subgroup_order, index, product, remainder, equal] 欄序回答。

查看答案與解釋(6, 3, 2, 6, 0, 是)

Wave6第五層核對=(6, 3, 2, 6, 0, 是)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0066/)

有限群的Lagrange定理 · qf-mod42-lagrange-divisibility-identity · candidate





## 67. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-divisibility-identity；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 [group_order, subgroup_order, index, product, remainder, equal] 欄序回答。

查看答案與解釋(8, 4, 2, 8, 0, 是)

Wave6第五層核對=(8, 4, 2, 8, 0, 是)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0067/)

有限群的Lagrange定理 · qf-mod42-lagrange-divisibility-identity · candidate





## 68. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-divisibility-identity；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":[1,3,5,7,9]}。請依 [group_order, subgroup_order, index, product, remainder, equal] 欄序回答。

查看答案與解釋(10, 5, 2, 10, 0, 是)

Wave6第五層核對=(10, 5, 2, 10, 0, 是)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0068/)

有限群的Lagrange定理 · qf-mod42-lagrange-divisibility-identity · candidate





## 69. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-divisibility-identity；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":[1,3,5,7,9,11]}。請依 [group_order, subgroup_order, index, product, remainder, equal] 欄序回答。

查看答案與解釋(12, 6, 2, 12, 0, 是)

Wave6第五層核對=(12, 6, 2, 12, 0, 是)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0069/)

有限群的Lagrange定理 · qf-mod42-lagrange-divisibility-identity · candidate





## 70. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-divisibility-identity；資料={"group_table":[[11,12,13,0,1,2,3,4,5,6,7,8,9,10],[12,13,0,1,2,3,4,5,6,7,8,9,10,11],[13,0,1,2,3,4,5,6,7,8,9,10,11,12],[0,1,2,3,4,5,6,7,8,9,10,11,12,13],[1,2,3,4,5,6,7,8,9,10,11,12,13,0],[2,3,4,5,6,7,8,9,10,11,12,13,0,1],[3,4,5,6,7,8,9,10,11,12,13,0,1,2],[4,5,6,7,8,9,10,11,12,13,0,1,2,3],[5,6,7,8,9,10,11,12,13,0,1,2,3,4],[6,7,8,9,10,11,12,13,0,1,2,3,4,5],[7,8,9,10,11,12,13,0,1,2,3,4,5,6],[8,9,10,11,12,13,0,1,2,3,4,5,6,7],[9,10,11,12,13,0,1,2,3,4,5,6,7,8],[10,11,12,13,0,1,2,3,4,5,6,7,8,9]],"identity":3,"subset":[1,3,5,7,9,11,13]}。請依 [group_order, subgroup_order, index, product, remainder, equal] 欄序回答。

查看答案與解釋(14, 7, 2, 14, 0, 是)

Wave6第五層核對=(14, 7, 2, 14, 0, 是)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0070/)

有限群的Lagrange定理 · qf-mod42-lagrange-divisibility-identity · candidate





## 71. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-divisibility-identity；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":[0,2,4]}。請依 [group_order, subgroup_order, index, product, remainder, equal] 欄序回答。

查看答案與解釋(6, 3, 2, 6, 0, 是)

Wave6第五層核對=(6, 3, 2, 6, 0, 是)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0071/)

有限群的Lagrange定理 · qf-mod42-lagrange-divisibility-identity · candidate





## 72. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-divisibility-identity；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 [group_order, subgroup_order, index, product, remainder, equal] 欄序回答。

查看答案與解釋(8, 4, 2, 8, 0, 是)

Wave6第五層核對=(8, 4, 2, 8, 0, 是)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0072/)

有限群的Lagrange定理 · qf-mod42-lagrange-divisibility-identity · candidate





## 73. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-divisibility-identity；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":[0,2,4,6,8]}。請依 [group_order, subgroup_order, index, product, remainder, equal] 欄序回答。

查看答案與解釋(10, 5, 2, 10, 0, 是)

Wave6第五層核對=(10, 5, 2, 10, 0, 是)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0073/)

有限群的Lagrange定理 · qf-mod42-lagrange-divisibility-identity · candidate





## 74. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-divisibility-identity；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":[0,2,4,6,8,10]}。請依 [group_order, subgroup_order, index, product, remainder, equal] 欄序回答。

查看答案與解釋(12, 6, 2, 12, 0, 是)

Wave6第五層核對=(12, 6, 2, 12, 0, 是)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0074/)

有限群的Lagrange定理 · qf-mod42-lagrange-divisibility-identity · candidate





## 75. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-divisibility-identity；資料={"group_table":[[10,11,12,13,0,1,2,3,4,5,6,7,8,9],[11,12,13,0,1,2,3,4,5,6,7,8,9,10],[12,13,0,1,2,3,4,5,6,7,8,9,10,11],[13,0,1,2,3,4,5,6,7,8,9,10,11,12],[0,1,2,3,4,5,6,7,8,9,10,11,12,13],[1,2,3,4,5,6,7,8,9,10,11,12,13,0],[2,3,4,5,6,7,8,9,10,11,12,13,0,1],[3,4,5,6,7,8,9,10,11,12,13,0,1,2],[4,5,6,7,8,9,10,11,12,13,0,1,2,3],[5,6,7,8,9,10,11,12,13,0,1,2,3,4],[6,7,8,9,10,11,12,13,0,1,2,3,4,5],[7,8,9,10,11,12,13,0,1,2,3,4,5,6],[8,9,10,11,12,13,0,1,2,3,4,5,6,7],[9,10,11,12,13,0,1,2,3,4,5,6,7,8]],"identity":4,"subset":[0,2,4,6,8,10,12]}。請依 [group_order, subgroup_order, index, product, remainder, equal] 欄序回答。

查看答案與解釋(14, 7, 2, 14, 0, 是)

Wave6第五層核對=(14, 7, 2, 14, 0, 是)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0075/)

有限群的Lagrange定理 · qf-mod42-lagrange-divisibility-identity · candidate





## 76. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-converse-boundary；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,"candidate_subset":[0,1]}。請依 [group_order, candidate_subset, candidate_size, size_divides_order, candidate_is_subgroup, general_converse_claim, boundary] 欄序回答。

size_divides_order、candidate_is_subgroup與最後的一般converse聲稱分開；固定的否不否定可能為是的subgroup旗標，也不證明或否定同階子群是否存在。

查看答案與解釋(6, [0, 1], 2, 是, 否, 否, divisor_sized_subset_need_not_be_a_subgroup_no_existence_converse_claim)

Wave6第五層核對=(6, [0, 1], 2, 是, 否, 否, divisor_sized_subset_need_not_be_a_subgroup_no_existence_converse_claim)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0076/)

有限群的Lagrange定理 · qf-mod42-lagrange-converse-boundary · candidate





## 77. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-converse-boundary；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,"candidate_subset":[0,1]}。請依 [group_order, candidate_subset, candidate_size, size_divides_order, candidate_is_subgroup, general_converse_claim, boundary] 欄序回答。

size_divides_order、candidate_is_subgroup與最後的一般converse聲稱分開；固定的否不否定可能為是的subgroup旗標，也不證明或否定同階子群是否存在。

查看答案與解釋(8, [0, 1], 2, 是, 否, 否, divisor_sized_subset_need_not_be_a_subgroup_no_existence_converse_claim)

Wave6第五層核對=(8, [0, 1], 2, 是, 否, 否, divisor_sized_subset_need_not_be_a_subgroup_no_existence_converse_claim)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0077/)

有限群的Lagrange定理 · qf-mod42-lagrange-converse-boundary · candidate





## 78. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-converse-boundary；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,"candidate_subset":[0,1]}。請依 [group_order, candidate_subset, candidate_size, size_divides_order, candidate_is_subgroup, general_converse_claim, boundary] 欄序回答。

size_divides_order、candidate_is_subgroup與最後的一般converse聲稱分開；固定的否不否定可能為是的subgroup旗標，也不證明或否定同階子群是否存在。

查看答案與解釋(10, [0, 1], 2, 是, 否, 否, divisor_sized_subset_need_not_be_a_subgroup_no_existence_converse_claim)

Wave6第五層核對=(10, [0, 1], 2, 是, 否, 否, divisor_sized_subset_need_not_be_a_subgroup_no_existence_converse_claim)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0078/)

有限群的Lagrange定理 · qf-mod42-lagrange-converse-boundary · candidate





## 79. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-converse-boundary；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,"candidate_subset":[0,1]}。請依 [group_order, candidate_subset, candidate_size, size_divides_order, candidate_is_subgroup, general_converse_claim, boundary] 欄序回答。

size_divides_order、candidate_is_subgroup與最後的一般converse聲稱分開；固定的否不否定可能為是的subgroup旗標，也不證明或否定同階子群是否存在。

查看答案與解釋(12, [0, 1], 2, 是, 否, 否, divisor_sized_subset_need_not_be_a_subgroup_no_existence_converse_claim)

Wave6第五層核對=(12, [0, 1], 2, 是, 否, 否, divisor_sized_subset_need_not_be_a_subgroup_no_existence_converse_claim)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0079/)

有限群的Lagrange定理 · qf-mod42-lagrange-converse-boundary · candidate





## 80. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-converse-boundary；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13],[1,2,3,4,5,6,7,8,9,10,11,12,13,0],[2,3,4,5,6,7,8,9,10,11,12,13,0,1],[3,4,5,6,7,8,9,10,11,12,13,0,1,2],[4,5,6,7,8,9,10,11,12,13,0,1,2,3],[5,6,7,8,9,10,11,12,13,0,1,2,3,4],[6,7,8,9,10,11,12,13,0,1,2,3,4,5],[7,8,9,10,11,12,13,0,1,2,3,4,5,6],[8,9,10,11,12,13,0,1,2,3,4,5,6,7],[9,10,11,12,13,0,1,2,3,4,5,6,7,8],[10,11,12,13,0,1,2,3,4,5,6,7,8,9],[11,12,13,0,1,2,3,4,5,6,7,8,9,10],[12,13,0,1,2,3,4,5,6,7,8,9,10,11],[13,0,1,2,3,4,5,6,7,8,9,10,11,12]],"identity":0,"candidate_subset":[0,1]}。請依 [group_order, candidate_subset, candidate_size, size_divides_order, candidate_is_subgroup, general_converse_claim, boundary] 欄序回答。

size_divides_order、candidate_is_subgroup與最後的一般converse聲稱分開；固定的否不否定可能為是的subgroup旗標，也不證明或否定同階子群是否存在。

查看答案與解釋(14, [0, 1], 2, 是, 否, 否, divisor_sized_subset_need_not_be_a_subgroup_no_existence_converse_claim)

Wave6第五層核對=(14, [0, 1], 2, 是, 否, 否, divisor_sized_subset_need_not_be_a_subgroup_no_existence_converse_claim)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0080/)

有限群的Lagrange定理 · qf-mod42-lagrange-converse-boundary · candidate





## 81. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-converse-boundary；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,"candidate_subset":[1,2]}。請依 [group_order, candidate_subset, candidate_size, size_divides_order, candidate_is_subgroup, general_converse_claim, boundary] 欄序回答。

size_divides_order、candidate_is_subgroup與最後的一般converse聲稱分開；固定的否不否定可能為是的subgroup旗標，也不證明或否定同階子群是否存在。

查看答案與解釋(6, [1, 2], 2, 是, 否, 否, divisor_sized_subset_need_not_be_a_subgroup_no_existence_converse_claim)

Wave6第五層核對=(6, [1, 2], 2, 是, 否, 否, divisor_sized_subset_need_not_be_a_subgroup_no_existence_converse_claim)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0081/)

有限群的Lagrange定理 · qf-mod42-lagrange-converse-boundary · candidate





## 82. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-converse-boundary；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,"candidate_subset":[1,2]}。請依 [group_order, candidate_subset, candidate_size, size_divides_order, candidate_is_subgroup, general_converse_claim, boundary] 欄序回答。

size_divides_order、candidate_is_subgroup與最後的一般converse聲稱分開；固定的否不否定可能為是的subgroup旗標，也不證明或否定同階子群是否存在。

查看答案與解釋(8, [1, 2], 2, 是, 否, 否, divisor_sized_subset_need_not_be_a_subgroup_no_existence_converse_claim)

Wave6第五層核對=(8, [1, 2], 2, 是, 否, 否, divisor_sized_subset_need_not_be_a_subgroup_no_existence_converse_claim)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0082/)

有限群的Lagrange定理 · qf-mod42-lagrange-converse-boundary · candidate





## 83. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-converse-boundary；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,"candidate_subset":[1,2]}。請依 [group_order, candidate_subset, candidate_size, size_divides_order, candidate_is_subgroup, general_converse_claim, boundary] 欄序回答。

size_divides_order、candidate_is_subgroup與最後的一般converse聲稱分開；固定的否不否定可能為是的subgroup旗標，也不證明或否定同階子群是否存在。

查看答案與解釋(10, [1, 2], 2, 是, 否, 否, divisor_sized_subset_need_not_be_a_subgroup_no_existence_converse_claim)

Wave6第五層核對=(10, [1, 2], 2, 是, 否, 否, divisor_sized_subset_need_not_be_a_subgroup_no_existence_converse_claim)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0083/)

有限群的Lagrange定理 · qf-mod42-lagrange-converse-boundary · candidate





## 84. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-converse-boundary；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,"candidate_subset":[1,2]}。請依 [group_order, candidate_subset, candidate_size, size_divides_order, candidate_is_subgroup, general_converse_claim, boundary] 欄序回答。

size_divides_order、candidate_is_subgroup與最後的一般converse聲稱分開；固定的否不否定可能為是的subgroup旗標，也不證明或否定同階子群是否存在。

查看答案與解釋(12, [1, 2], 2, 是, 否, 否, divisor_sized_subset_need_not_be_a_subgroup_no_existence_converse_claim)

Wave6第五層核對=(12, [1, 2], 2, 是, 否, 否, divisor_sized_subset_need_not_be_a_subgroup_no_existence_converse_claim)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0084/)

有限群的Lagrange定理 · qf-mod42-lagrange-converse-boundary · candidate





## 85. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-converse-boundary；資料={"group_table":[[13,0,1,2,3,4,5,6,7,8,9,10,11,12],[0,1,2,3,4,5,6,7,8,9,10,11,12,13],[1,2,3,4,5,6,7,8,9,10,11,12,13,0],[2,3,4,5,6,7,8,9,10,11,12,13,0,1],[3,4,5,6,7,8,9,10,11,12,13,0,1,2],[4,5,6,7,8,9,10,11,12,13,0,1,2,3],[5,6,7,8,9,10,11,12,13,0,1,2,3,4],[6,7,8,9,10,11,12,13,0,1,2,3,4,5],[7,8,9,10,11,12,13,0,1,2,3,4,5,6],[8,9,10,11,12,13,0,1,2,3,4,5,6,7],[9,10,11,12,13,0,1,2,3,4,5,6,7,8],[10,11,12,13,0,1,2,3,4,5,6,7,8,9],[11,12,13,0,1,2,3,4,5,6,7,8,9,10],[12,13,0,1,2,3,4,5,6,7,8,9,10,11]],"identity":1,"candidate_subset":[1,2]}。請依 [group_order, candidate_subset, candidate_size, size_divides_order, candidate_is_subgroup, general_converse_claim, boundary] 欄序回答。

size_divides_order、candidate_is_subgroup與最後的一般converse聲稱分開；固定的否不否定可能為是的subgroup旗標，也不證明或否定同階子群是否存在。

查看答案與解釋(14, [1, 2], 2, 是, 否, 否, divisor_sized_subset_need_not_be_a_subgroup_no_existence_converse_claim)

Wave6第五層核對=(14, [1, 2], 2, 是, 否, 否, divisor_sized_subset_need_not_be_a_subgroup_no_existence_converse_claim)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0085/)

有限群的Lagrange定理 · qf-mod42-lagrange-converse-boundary · candidate





## 86. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-converse-boundary；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,"candidate_subset":[2,3]}。請依 [group_order, candidate_subset, candidate_size, size_divides_order, candidate_is_subgroup, general_converse_claim, boundary] 欄序回答。

size_divides_order、candidate_is_subgroup與最後的一般converse聲稱分開；固定的否不否定可能為是的subgroup旗標，也不證明或否定同階子群是否存在。

查看答案與解釋(6, [2, 3], 2, 是, 否, 否, divisor_sized_subset_need_not_be_a_subgroup_no_existence_converse_claim)

Wave6第五層核對=(6, [2, 3], 2, 是, 否, 否, divisor_sized_subset_need_not_be_a_subgroup_no_existence_converse_claim)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0086/)

有限群的Lagrange定理 · qf-mod42-lagrange-converse-boundary · candidate





## 87. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-converse-boundary；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,"candidate_subset":[2,3]}。請依 [group_order, candidate_subset, candidate_size, size_divides_order, candidate_is_subgroup, general_converse_claim, boundary] 欄序回答。

size_divides_order、candidate_is_subgroup與最後的一般converse聲稱分開；固定的否不否定可能為是的subgroup旗標，也不證明或否定同階子群是否存在。

查看答案與解釋(8, [2, 3], 2, 是, 否, 否, divisor_sized_subset_need_not_be_a_subgroup_no_existence_converse_claim)

Wave6第五層核對=(8, [2, 3], 2, 是, 否, 否, divisor_sized_subset_need_not_be_a_subgroup_no_existence_converse_claim)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0087/)

有限群的Lagrange定理 · qf-mod42-lagrange-converse-boundary · candidate





## 88. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-converse-boundary；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,"candidate_subset":[2,3]}。請依 [group_order, candidate_subset, candidate_size, size_divides_order, candidate_is_subgroup, general_converse_claim, boundary] 欄序回答。

size_divides_order、candidate_is_subgroup與最後的一般converse聲稱分開；固定的否不否定可能為是的subgroup旗標，也不證明或否定同階子群是否存在。

查看答案與解釋(10, [2, 3], 2, 是, 否, 否, divisor_sized_subset_need_not_be_a_subgroup_no_existence_converse_claim)

Wave6第五層核對=(10, [2, 3], 2, 是, 否, 否, divisor_sized_subset_need_not_be_a_subgroup_no_existence_converse_claim)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0088/)

有限群的Lagrange定理 · qf-mod42-lagrange-converse-boundary · candidate





## 89. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-converse-boundary；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,"candidate_subset":[2,3]}。請依 [group_order, candidate_subset, candidate_size, size_divides_order, candidate_is_subgroup, general_converse_claim, boundary] 欄序回答。

size_divides_order、candidate_is_subgroup與最後的一般converse聲稱分開；固定的否不否定可能為是的subgroup旗標，也不證明或否定同階子群是否存在。

查看答案與解釋(12, [2, 3], 2, 是, 否, 否, divisor_sized_subset_need_not_be_a_subgroup_no_existence_converse_claim)

Wave6第五層核對=(12, [2, 3], 2, 是, 否, 否, divisor_sized_subset_need_not_be_a_subgroup_no_existence_converse_claim)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0089/)

有限群的Lagrange定理 · qf-mod42-lagrange-converse-boundary · candidate





## 90. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-converse-boundary；資料={"group_table":[[12,13,0,1,2,3,4,5,6,7,8,9,10,11],[13,0,1,2,3,4,5,6,7,8,9,10,11,12],[0,1,2,3,4,5,6,7,8,9,10,11,12,13],[1,2,3,4,5,6,7,8,9,10,11,12,13,0],[2,3,4,5,6,7,8,9,10,11,12,13,0,1],[3,4,5,6,7,8,9,10,11,12,13,0,1,2],[4,5,6,7,8,9,10,11,12,13,0,1,2,3],[5,6,7,8,9,10,11,12,13,0,1,2,3,4],[6,7,8,9,10,11,12,13,0,1,2,3,4,5],[7,8,9,10,11,12,13,0,1,2,3,4,5,6],[8,9,10,11,12,13,0,1,2,3,4,5,6,7],[9,10,11,12,13,0,1,2,3,4,5,6,7,8],[10,11,12,13,0,1,2,3,4,5,6,7,8,9],[11,12,13,0,1,2,3,4,5,6,7,8,9,10]],"identity":2,"candidate_subset":[2,3]}。請依 [group_order, candidate_subset, candidate_size, size_divides_order, candidate_is_subgroup, general_converse_claim, boundary] 欄序回答。

size_divides_order、candidate_is_subgroup與最後的一般converse聲稱分開；固定的否不否定可能為是的subgroup旗標，也不證明或否定同階子群是否存在。

查看答案與解釋(14, [2, 3], 2, 是, 否, 否, divisor_sized_subset_need_not_be_a_subgroup_no_existence_converse_claim)

Wave6第五層核對=(14, [2, 3], 2, 是, 否, 否, divisor_sized_subset_need_not_be_a_subgroup_no_existence_converse_claim)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0090/)

有限群的Lagrange定理 · qf-mod42-lagrange-converse-boundary · candidate





## 91. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-converse-boundary；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,"candidate_subset":[3,4]}。請依 [group_order, candidate_subset, candidate_size, size_divides_order, candidate_is_subgroup, general_converse_claim, boundary] 欄序回答。

size_divides_order、candidate_is_subgroup與最後的一般converse聲稱分開；固定的否不否定可能為是的subgroup旗標，也不證明或否定同階子群是否存在。

查看答案與解釋(6, [3, 4], 2, 是, 否, 否, divisor_sized_subset_need_not_be_a_subgroup_no_existence_converse_claim)

Wave6第五層核對=(6, [3, 4], 2, 是, 否, 否, divisor_sized_subset_need_not_be_a_subgroup_no_existence_converse_claim)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0091/)

有限群的Lagrange定理 · qf-mod42-lagrange-converse-boundary · candidate





## 92. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-converse-boundary；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,"candidate_subset":[3,4]}。請依 [group_order, candidate_subset, candidate_size, size_divides_order, candidate_is_subgroup, general_converse_claim, boundary] 欄序回答。

size_divides_order、candidate_is_subgroup與最後的一般converse聲稱分開；固定的否不否定可能為是的subgroup旗標，也不證明或否定同階子群是否存在。

查看答案與解釋(8, [3, 4], 2, 是, 否, 否, divisor_sized_subset_need_not_be_a_subgroup_no_existence_converse_claim)

Wave6第五層核對=(8, [3, 4], 2, 是, 否, 否, divisor_sized_subset_need_not_be_a_subgroup_no_existence_converse_claim)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0092/)

有限群的Lagrange定理 · qf-mod42-lagrange-converse-boundary · candidate





## 93. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-converse-boundary；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,"candidate_subset":[3,4]}。請依 [group_order, candidate_subset, candidate_size, size_divides_order, candidate_is_subgroup, general_converse_claim, boundary] 欄序回答。

size_divides_order、candidate_is_subgroup與最後的一般converse聲稱分開；固定的否不否定可能為是的subgroup旗標，也不證明或否定同階子群是否存在。

查看答案與解釋(10, [3, 4], 2, 是, 否, 否, divisor_sized_subset_need_not_be_a_subgroup_no_existence_converse_claim)

Wave6第五層核對=(10, [3, 4], 2, 是, 否, 否, divisor_sized_subset_need_not_be_a_subgroup_no_existence_converse_claim)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0093/)

有限群的Lagrange定理 · qf-mod42-lagrange-converse-boundary · candidate





## 94. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-converse-boundary；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,"candidate_subset":[3,4]}。請依 [group_order, candidate_subset, candidate_size, size_divides_order, candidate_is_subgroup, general_converse_claim, boundary] 欄序回答。

size_divides_order、candidate_is_subgroup與最後的一般converse聲稱分開；固定的否不否定可能為是的subgroup旗標，也不證明或否定同階子群是否存在。

查看答案與解釋(12, [3, 4], 2, 是, 否, 否, divisor_sized_subset_need_not_be_a_subgroup_no_existence_converse_claim)

Wave6第五層核對=(12, [3, 4], 2, 是, 否, 否, divisor_sized_subset_need_not_be_a_subgroup_no_existence_converse_claim)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0094/)

有限群的Lagrange定理 · qf-mod42-lagrange-converse-boundary · candidate





## 95. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-converse-boundary；資料={"group_table":[[11,12,13,0,1,2,3,4,5,6,7,8,9,10],[12,13,0,1,2,3,4,5,6,7,8,9,10,11],[13,0,1,2,3,4,5,6,7,8,9,10,11,12],[0,1,2,3,4,5,6,7,8,9,10,11,12,13],[1,2,3,4,5,6,7,8,9,10,11,12,13,0],[2,3,4,5,6,7,8,9,10,11,12,13,0,1],[3,4,5,6,7,8,9,10,11,12,13,0,1,2],[4,5,6,7,8,9,10,11,12,13,0,1,2,3],[5,6,7,8,9,10,11,12,13,0,1,2,3,4],[6,7,8,9,10,11,12,13,0,1,2,3,4,5],[7,8,9,10,11,12,13,0,1,2,3,4,5,6],[8,9,10,11,12,13,0,1,2,3,4,5,6,7],[9,10,11,12,13,0,1,2,3,4,5,6,7,8],[10,11,12,13,0,1,2,3,4,5,6,7,8,9]],"identity":3,"candidate_subset":[3,4]}。請依 [group_order, candidate_subset, candidate_size, size_divides_order, candidate_is_subgroup, general_converse_claim, boundary] 欄序回答。

size_divides_order、candidate_is_subgroup與最後的一般converse聲稱分開；固定的否不否定可能為是的subgroup旗標，也不證明或否定同階子群是否存在。

查看答案與解釋(14, [3, 4], 2, 是, 否, 否, divisor_sized_subset_need_not_be_a_subgroup_no_existence_converse_claim)

Wave6第五層核對=(14, [3, 4], 2, 是, 否, 否, divisor_sized_subset_need_not_be_a_subgroup_no_existence_converse_claim)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0095/)

有限群的Lagrange定理 · qf-mod42-lagrange-converse-boundary · candidate





## 96. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-converse-boundary；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,"candidate_subset":[4,5]}。請依 [group_order, candidate_subset, candidate_size, size_divides_order, candidate_is_subgroup, general_converse_claim, boundary] 欄序回答。

size_divides_order、candidate_is_subgroup與最後的一般converse聲稱分開；固定的否不否定可能為是的subgroup旗標，也不證明或否定同階子群是否存在。

查看答案與解釋(6, [4, 5], 2, 是, 否, 否, divisor_sized_subset_need_not_be_a_subgroup_no_existence_converse_claim)

Wave6第五層核對=(6, [4, 5], 2, 是, 否, 否, divisor_sized_subset_need_not_be_a_subgroup_no_existence_converse_claim)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0096/)

有限群的Lagrange定理 · qf-mod42-lagrange-converse-boundary · candidate





## 97. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-converse-boundary；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,"candidate_subset":[4,5]}。請依 [group_order, candidate_subset, candidate_size, size_divides_order, candidate_is_subgroup, general_converse_claim, boundary] 欄序回答。

size_divides_order、candidate_is_subgroup與最後的一般converse聲稱分開；固定的否不否定可能為是的subgroup旗標，也不證明或否定同階子群是否存在。

查看答案與解釋(8, [4, 5], 2, 是, 否, 否, divisor_sized_subset_need_not_be_a_subgroup_no_existence_converse_claim)

Wave6第五層核對=(8, [4, 5], 2, 是, 否, 否, divisor_sized_subset_need_not_be_a_subgroup_no_existence_converse_claim)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0097/)

有限群的Lagrange定理 · qf-mod42-lagrange-converse-boundary · candidate





## 98. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-converse-boundary；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,"candidate_subset":[4,5]}。請依 [group_order, candidate_subset, candidate_size, size_divides_order, candidate_is_subgroup, general_converse_claim, boundary] 欄序回答。

size_divides_order、candidate_is_subgroup與最後的一般converse聲稱分開；固定的否不否定可能為是的subgroup旗標，也不證明或否定同階子群是否存在。

查看答案與解釋(10, [4, 5], 2, 是, 否, 否, divisor_sized_subset_need_not_be_a_subgroup_no_existence_converse_claim)

Wave6第五層核對=(10, [4, 5], 2, 是, 否, 否, divisor_sized_subset_need_not_be_a_subgroup_no_existence_converse_claim)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0098/)

有限群的Lagrange定理 · qf-mod42-lagrange-converse-boundary · candidate





## 99. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-converse-boundary；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,"candidate_subset":[4,5]}。請依 [group_order, candidate_subset, candidate_size, size_divides_order, candidate_is_subgroup, general_converse_claim, boundary] 欄序回答。

size_divides_order、candidate_is_subgroup與最後的一般converse聲稱分開；固定的否不否定可能為是的subgroup旗標，也不證明或否定同階子群是否存在。

查看答案與解釋(12, [4, 5], 2, 是, 否, 否, divisor_sized_subset_need_not_be_a_subgroup_no_existence_converse_claim)

Wave6第五層核對=(12, [4, 5], 2, 是, 否, 否, divisor_sized_subset_need_not_be_a_subgroup_no_existence_converse_claim)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0099/)

有限群的Lagrange定理 · qf-mod42-lagrange-converse-boundary · candidate





## 100. 有限群的Lagrange定理

完整有限Cayley table、完整subgroup證書與全部left cosets。操作=lagrange-converse-boundary；資料={"group_table":[[10,11,12,13,0,1,2,3,4,5,6,7,8,9],[11,12,13,0,1,2,3,4,5,6,7,8,9,10],[12,13,0,1,2,3,4,5,6,7,8,9,10,11],[13,0,1,2,3,4,5,6,7,8,9,10,11,12],[0,1,2,3,4,5,6,7,8,9,10,11,12,13],[1,2,3,4,5,6,7,8,9,10,11,12,13,0],[2,3,4,5,6,7,8,9,10,11,12,13,0,1],[3,4,5,6,7,8,9,10,11,12,13,0,1,2],[4,5,6,7,8,9,10,11,12,13,0,1,2,3],[5,6,7,8,9,10,11,12,13,0,1,2,3,4],[6,7,8,9,10,11,12,13,0,1,2,3,4,5],[7,8,9,10,11,12,13,0,1,2,3,4,5,6],[8,9,10,11,12,13,0,1,2,3,4,5,6,7],[9,10,11,12,13,0,1,2,3,4,5,6,7,8]],"identity":4,"candidate_subset":[4,5]}。請依 [group_order, candidate_subset, candidate_size, size_divides_order, candidate_is_subgroup, general_converse_claim, boundary] 欄序回答。

size_divides_order、candidate_is_subgroup與最後的一般converse聲稱分開；固定的否不否定可能為是的subgroup旗標，也不證明或否定同階子群是否存在。

查看答案與解釋(14, [4, 5], 2, 是, 否, 否, divisor_sized_subset_need_not_be_a_subgroup_no_existence_converse_claim)

Wave6第五層核對=(14, [4, 5], 2, 是, 否, 否, divisor_sized_subset_need_not_be_a_subgroup_no_existence_converse_claim)；依完整明示資料獨立重算；left cosets必須相等或不交、覆蓋G且每個由H到gH的平移是bijection；本family只證divisor-sized指定subset不必是subgroup；不據此證明或否定同階subgroup的存在。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-0100/)

有限群的Lagrange定理 · qf-mod42-lagrange-converse-boundary · candidate



[原始題目 JSONL](https://ocme.evemisslab.com/data/questions/batches/batch-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-foundations/questions.jsonl) · [驗收報告](https://ocme.evemisslab.com/data/questions/batches/batch-20261014-advance-20261111-r01-lagrange-theorem-finite-groups-foundations/validation-report.json)