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
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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。
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(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）
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。
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(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）
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。
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(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）
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。
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(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）
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。
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(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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
有限群的Lagrange定理 · qf-mod42-lagrange-converse-boundary · candidate
原始題目 JSONL · 驗收報告