# 第 25747 題：有限群第一同構定理 [返回所在分頁 129](https://ocme.evemisslab.com/zh-Hant/questions/page/129/) [← 逐題詳解目錄](https://ocme.evemisslab.com/zh-Hant/questions/) · [原題批次](https://ocme.evemisslab.com/zh-Hant/practice/batch-20261015-advance-20261115-r01-first-isomorphism-theorem-finite-groups-foundations/#q-20261015-advance-20261115-r01-first-isomorphism-theorem-finite-groups-0097) 本頁是已完成第二對話 AI 數理與中英語義覆核的教學詳解，只支持本題明示的模型與前提。沒有人工審查或新 Lean 證明，也不提升原題或 MKO 的 Canonical 真值狀態。 R0050-25747 · q-20261015-advance-20261115-r01-first-isomorphism-theorem-finite-groups-0097 ## 原題與已知條件 完整有限群、total homomorphism、kernel、image與quotient cosets的第一同構責任。操作=iso1-image-codomain-boundary；資料={"source_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,0],[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,0,1],[3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,0,1,2],[4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,0,1,2,3],[5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,0,1,2,3,4],[6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,0,1,2,3,4,5],[7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,0,1,2,3,4,5,6],[8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,0,1,2,3,4,5,6,7],[9,10,11,12,13,14,15,16,17,18,19,20,21,22,0,1,2,3,4,5,6,7,8],[10,11,12,13,14,15,16,17,18,19,20,21,22,0,1,2,3,4,5,6,7,8,9],[11,12,13,14,15,16,17,18,19,20,21,22,0,1,2,3,4,5,6,7,8,9,10],[12,13,14,15,16,17,18,19,20,21,22,0,1,2,3,4,5,6,7,8,9,10,11],[13,14,15,16,17,18,19,20,21,22,0,1,2,3,4,5,6,7,8,9,10,11,12],[14,15,16,17,18,19,20,21,22,0,1,2,3,4,5,6,7,8,9,10,11,12,13],[15,16,17,18,19,20,21,22,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14],[16,17,18,19,20,21,22,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],[17,18,19,20,21,22,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16],[18,19,20,21,22,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17],[19,20,21,22,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18],[20,21,22,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19],[21,22,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20],[22,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21]],"source_identity":0,"target_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,0],[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,0,1],[3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,0,1,2],[4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,0,1,2,3],[5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,0,1,2,3,4],[6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,0,1,2,3,4,5],[7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,0,1,2,3,4,5,6],[8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,0,1,2,3,4,5,6,7],[9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,0,1,2,3,4,5,6,7,8],[10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,0,1,2,3,4,5,6,7,8,9],[11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,0,1,2,3,4,5,6,7,8,9,10],[12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,0,1,2,3,4,5,6,7,8,9,10,11],[13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,0,1,2,3,4,5,6,7,8,9,10,11,12],[14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,0,1,2,3,4,5,6,7,8,9,10,11,12,13],[15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14],[16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],[17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16],[18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17],[19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18],[20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19],[21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20],[22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21],[23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22],[24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23],[25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24],[26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25],[27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26],[28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27],[29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28],[30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29],[31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30],[32,33,34,35,36,37,38,39,40,41,42,43,44,45,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31],[33,34,35,36,37,38,39,40,41,42,43,44,45,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32],[34,35,36,37,38,39,40,41,42,43,44,45,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33],[35,36,37,38,39,40,41,42,43,44,45,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34],[36,37,38,39,40,41,42,43,44,45,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35],[37,38,39,40,41,42,43,44,45,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36],[38,39,40,41,42,43,44,45,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37],[39,40,41,42,43,44,45,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38],[40,41,42,43,44,45,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39],[41,42,43,44,45,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40],[42,43,44,45,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41],[43,44,45,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42],[44,45,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],[45,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44]],"target_identity":0,"mapping":[0,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。 - G001 — 完整有限群、total homomorphism、kernel、image與quotient cosets的第一同構責任。操作=iso1-image-codomain-boundary；資料={"source_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,0],[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,0,1],[3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,0,1,2],[4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,0,1,2,3],[5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,0,1,2,3,4],[6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,0,1,2,3,4,5],[7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,0,1,2,3,4,5,6],[8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,0,1,2,3,4,5,6,7],[9,10,11,12,13,14,15,16,17,18,19,20,21,22,0,1,2,3,4,5,6,7,8],[10,11,12,13,14,15,16,17,18,19,20,21,22,0,1,2,3,4,5,6,7,8,9],[11,12,13,14,15,16,17,18,19,20,21,22,0,1,2,3,4,5,6,7,8,9,10],[12,13,14,15,16,17,18,19,20,21,22,0,1,2,3,4,5,6,7,8,9,10,11],[13,14,15,16,17,18,19,20,21,22,0,1,2,3,4,5,6,7,8,9,10,11,12],[14,15,16,17,18,19,20,21,22,0,1,2,3,4,5,6,7,8,9,10,11,12,13],[15,16,17,18,19,20,21,22,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14],[16,17,18,19,20,21,22,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],[17,18,19,20,21,22,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16],[18,19,20,21,22,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17],[19,20,21,22,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18],[20,21,22,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19],[21,22,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20],[22,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21]],"source_identity":0,"target_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,0],[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,0,1],[3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,0,1,2],[4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,0,1,2,3],[5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,0,1,2,3,4],[6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,0,1,2,3,4,5],[7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,0,1,2,3,4,5,6],[8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,0,1,2,3,4,5,6,7],[9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,0,1,2,3,4,5,6,7,8],[10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,0,1,2,3,4,5,6,7,8,9],[11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,0,1,2,3,4,5,6,7,8,9,10],[12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,0,1,2,3,4,5,6,7,8,9,10,11],[13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,0,1,2,3,4,5,6,7,8,9,10,11,12],[14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,0,1,2,3,4,5,6,7,8,9,10,11,12,13],[15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14],[16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],[17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16],[18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17],[19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18],[20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19],[21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20],[22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21],[23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22],[24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23],[25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24],[26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25],[27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26],[28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27],[29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28],[30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29],[31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30],[32,33,34,35,36,37,38,39,40,41,42,43,44,45,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31],[33,34,35,36,37,38,39,40,41,42,43,44,45,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32],[34,35,36,37,38,39,40,41,42,43,44,45,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33],[35,36,37,38,39,40,41,42,43,44,45,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34],[36,37,38,39,40,41,42,43,44,45,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35],[37,38,39,40,41,42,43,44,45,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36],[38,39,40,41,42,43,44,45,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37],[39,40,41,42,43,44,45,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38],[40,41,42,43,44,45,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39],[41,42,43,44,45,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40],[42,43,44,45,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41],[43,44,45,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42],[44,45,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],[45,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44]],"target_identity":0,"mapping":[0,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。 ## 定義與適用範圍 沿用原題明示的論域、假設與來源 MKO 定義。本題已完成第二對話數理與中英語義覆核，並由原始參數逐題獨立重算模型、答案與每個算術步驟；原題仍為 candidate。 - [mko-first-isomorphism-theorem-finite-groups](https://ocme.evemisslab.com/zh-Hant/mko/mko-first-isomorphism-theorem-finite-groups/) ## 逐步推導 S001 · implies操作前 source roles = [iso1-image-codomain-boundary] 操作後 derived = [[image, codomain_order, image_order, surjective_to_codomain, image_isomorphism_statement, codomain_scope, general_theorem_proof_claim, boundary]] 條件：無 直接列完整來源欄序，不需JavaScript。LP weak為13欄、zero與strong為15欄，前提與角色依原operation／mode，不補欄。 步驟識別與依賴規則：source_ordered_fields_without_JS · 依賴：G001 S002 · implies操作前 source roles = [Iso1 ORIGINAL SOURCE, [[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 0], [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 0, 1], [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 0, 1, 2], [4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 0, 1, 2, 3], [5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 0, 1, 2, 3, 4], [6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 0, 1, 2, 3, 4, 5], [7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 0, 1, 2, 3, 4, 5, 6], [8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 0, 1, 2, 3, 4, 5, 6, 7], [9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 0, 1, 2, 3, 4, 5, 6, 7, 8], [10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10], [12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], [14, 15, 16, 17, 18, 19, 20, 21, 22, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13], [15, 16, 17, 18, 19, 20, 21, 22, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14], [16, 17, 18, 19, 20, 21, 22, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15], [17, 18, 19, 20, 21, 22, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16], [18, 19, 20, 21, 22, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17], [19, 20, 21, 22, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18], [20, 21, 22, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19], [21, 22, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20], [22, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21]], 0] 操作後 derived = [23, [[0, 0, 0, 0], [1, 1, 1, 1], [2, 2, 2, 2], [3, 3, 3, 3], [4, 4, 4, 4], [5, 5, 5, 5], [6, 6, 6, 6], [7, 7, 7, 7], [8, 8, 8, 8], [9, 9, 9, 9], [10, 10, 10, 10], [11, 11, 11, 11], [12, 12, 12, 12], [13, 13, 13, 13], [14, 14, 14, 14], [15, 15, 15, 15], [16, 16, 16, 16], [17, 17, 17, 17], [18, 18, 18, 18], [19, 19, 19, 19], [20, 20, 20, 20], [21, 21, 21, 21], [22, 22, 22, 22]], 是] 條件：無 完整closed Cayley table與實際identity先資格核對，群階可到64，不假設identity0。 步驟識別與依賴規則：Group_complete_table_actual_identity_bound64 · 依賴：G001, S001 S003 · implies操作前 source roles = [Iso1 ORIGINAL SOURCE, 23, 0] 操作後 derived = [[[是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是]], 12167, [0, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]] 條件：無 每pair格逐全部第三元素核結合律，完整n³而非抽樣；inverse同時左右回實際identity。 步驟識別與依賴規則：Group_ALL_triples_compact_pair_matrix_and_ALL_inverses · 依賴：G001, S002 S004 · implies操作前 source roles = [Iso1 ORIGINAL TARGET, [[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 0], [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 0, 1], [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 0, 1, 2], [4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 0, 1, 2, 3], [5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 0, 1, 2, 3, 4], [6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 0, 1, 2, 3, 4, 5], [7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 0, 1, 2, 3, 4, 5, 6], [8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 0, 1, 2, 3, 4, 5, 6, 7], [9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 0, 1, 2, 3, 4, 5, 6, 7, 8], [10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10], [12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], [14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13], [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14], [16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15], [17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16], [18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17], [19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18], [20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19], [21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20], [22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21], [23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22], [24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23], [25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24], [26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25], [27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26], [28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27], [29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28], [30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29], [31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30], [32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31], [33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32], [34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33], [35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34], [36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35], [37, 38, 39, 40, 41, 42, 43, 44, 45, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36], [38, 39, 40, 41, 42, 43, 44, 45, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37], [39, 40, 41, 42, 43, 44, 45, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38], [40, 41, 42, 43, 44, 45, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39], [41, 42, 43, 44, 45, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40], [42, 43, 44, 45, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41], [43, 44, 45, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42], [44, 45, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43], [45, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44]], 0] 操作後 derived = [46, [[0, 0, 0, 0], [1, 1, 1, 1], [2, 2, 2, 2], [3, 3, 3, 3], [4, 4, 4, 4], [5, 5, 5, 5], [6, 6, 6, 6], [7, 7, 7, 7], [8, 8, 8, 8], [9, 9, 9, 9], [10, 10, 10, 10], [11, 11, 11, 11], [12, 12, 12, 12], [13, 13, 13, 13], [14, 14, 14, 14], [15, 15, 15, 15], [16, 16, 16, 16], [17, 17, 17, 17], [18, 18, 18, 18], [19, 19, 19, 19], [20, 20, 20, 20], [21, 21, 21, 21], [22, 22, 22, 22], [23, 23, 23, 23], [24, 24, 24, 24], [25, 25, 25, 25], [26, 26, 26, 26], [27, 27, 27, 27], [28, 28, 28, 28], [29, 29, 29, 29], [30, 30, 30, 30], [31, 31, 31, 31], [32, 32, 32, 32], [33, 33, 33, 33], [34, 34, 34, 34], [35, 35, 35, 35], [36, 36, 36, 36], [37, 37, 37, 37], [38, 38, 38, 38], [39, 39, 39, 39], [40, 40, 40, 40], [41, 41, 41, 41], [42, 42, 42, 42], [43, 43, 43, 43], [44, 44, 44, 44], [45, 45, 45, 45]], 是] 條件：無 完整closed Cayley table與實際identity先資格核對，群階可到64，不假設identity0。 步驟識別與依賴規則：Group_complete_table_actual_identity_bound64 · 依賴：G001, S003 S005 · implies操作前 source roles = [Iso1 ORIGINAL TARGET, 46, 0] 操作後 derived = [[[是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 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是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是]], 97336, [0, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]] 條件：無 每pair格逐全部第三元素核結合律，完整n³而非抽樣；inverse同時左右回實際identity。 步驟識別與依賴規則：Group_ALL_triples_compact_pair_matrix_and_ALL_inverses · 依賴：G001, S004 S006 · implies操作前 source roles = [Iso1 ACTUAL kernel, [0], 0] 操作後 derived = [是, [[0, 0, 0, 是]], 是, [[0, 0, 是]], 是, 是, [[0, [0], 是], [1, [0], 是], [2, [0], 是], [3, [0], 是], [4, [0], 是], [5, [0], 是], [6, [0], 是], [7, [0], 是], [8, [0], 是], [9, [0], 是], [10, [0], 是], [11, [0], 是], [12, [0], 是], [13, [0], 是], [14, [0], 是], [15, [0], 是], [16, [0], 是], [17, [0], 是], [18, [0], 是], [19, [0], 是], [20, [0], 是], [21, [0], 是], [22, [0], 是]], 是] 條件：無 含identity、全部product與inverse closure各核，三者合取才成subgroup；再逐全部g驗normal。即使某map失敗，這些實際property仍可分別True，不由定理名稱填旗標。 步驟識別與依賴規則：Subgroup_actual_identity_product_inverse_ALL_conjugates · 依賴：G001, S005 S007 · implies操作前 source roles = [Iso1 ACTUAL image, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44], 0] 操作後 derived = [是, [[0, 0, 0, 是], [0, 2, 2, 是], [0, 4, 4, 是], [0, 6, 6, 是], [0, 8, 8, 是], [0, 10, 10, 是], [0, 12, 12, 是], [0, 14, 14, 是], [0, 16, 16, 是], [0, 18, 18, 是], [0, 20, 20, 是], [0, 22, 22, 是], [0, 24, 24, 是], [0, 26, 26, 是], [0, 28, 28, 是], [0, 30, 30, 是], [0, 32, 32, 是], [0, 34, 34, 是], [0, 36, 36, 是], [0, 38, 38, 是], [0, 40, 40, 是], [0, 42, 42, 是], [0, 44, 44, 是], [2, 0, 2, 是], [2, 2, 4, 是], [2, 4, 6, 是], [2, 6, 8, 是], [2, 8, 10, 是], [2, 10, 12, 是], [2, 12, 14, 是], [2, 14, 16, 是], [2, 16, 18, 是], [2, 18, 20, 是], [2, 20, 22, 是], [2, 22, 24, 是], [2, 24, 26, 是], [2, 26, 28, 是], [2, 28, 30, 是], [2, 30, 32, 是], [2, 32, 34, 是], [2, 34, 36, 是], [2, 36, 38, 是], [2, 38, 40, 是], [2, 40, 42, 是], [2, 42, 44, 是], [2, 44, 0, 是], [4, 0, 4, 是], [4, 2, 6, 是], [4, 4, 8, 是], [4, 6, 10, 是], [4, 8, 12, 是], [4, 10, 14, 是], [4, 12, 16, 是], [4, 14, 18, 是], [4, 16, 20, 是], [4, 18, 22, 是], [4, 20, 24, 是], [4, 22, 26, 是], [4, 24, 28, 是], [4, 26, 30, 是], [4, 28, 32, 是], [4, 30, 34, 是], [4, 32, 36, 是], [4, 34, 38, 是], [4, 36, 40, 是], [4, 38, 42, 是], [4, 40, 44, 是], [4, 42, 0, 是], [4, 44, 2, 是], [6, 0, 6, 是], [6, 2, 8, 是], [6, 4, 10, 是], [6, 6, 12, 是], [6, 8, 14, 是], [6, 10, 16, 是], [6, 12, 18, 是], [6, 14, 20, 是], [6, 16, 22, 是], [6, 18, 24, 是], [6, 20, 26, 是], [6, 22, 28, 是], [6, 24, 30, 是], [6, 26, 32, 是], [6, 28, 34, 是], [6, 30, 36, 是], [6, 32, 38, 是], [6, 34, 40, 是], [6, 36, 42, 是], [6, 38, 44, 是], [6, 40, 0, 是], [6, 42, 2, 是], [6, 44, 4, 是], [8, 0, 8, 是], [8, 2, 10, 是], [8, 4, 12, 是], [8, 6, 14, 是], [8, 8, 16, 是], [8, 10, 18, 是], [8, 12, 20, 是], [8, 14, 22, 是], [8, 16, 24, 是], [8, 18, 26, 是], [8, 20, 28, 是], [8, 22, 30, 是], [8, 24, 32, 是], [8, 26, 34, 是], [8, 28, 36, 是], [8, 30, 38, 是], [8, 32, 40, 是], [8, 34, 42, 是], [8, 36, 44, 是], [8, 38, 0, 是], [8, 40, 2, 是], [8, 42, 4, 是], [8, 44, 6, 是], [10, 0, 10, 是], [10, 2, 12, 是], [10, 4, 14, 是], [10, 6, 16, 是], [10, 8, 18, 是], [10, 10, 20, 是], [10, 12, 22, 是], [10, 14, 24, 是], [10, 16, 26, 是], [10, 18, 28, 是], [10, 20, 30, 是], [10, 22, 32, 是], [10, 24, 34, 是], [10, 26, 36, 是], [10, 28, 38, 是], [10, 30, 40, 是], [10, 32, 42, 是], [10, 34, 44, 是], [10, 36, 0, 是], [10, 38, 2, 是], [10, 40, 4, 是], [10, 42, 6, 是], [10, 44, 8, 是], [12, 0, 12, 是], [12, 2, 14, 是], [12, 4, 16, 是], [12, 6, 18, 是], [12, 8, 20, 是], [12, 10, 22, 是], [12, 12, 24, 是], [12, 14, 26, 是], [12, 16, 28, 是], [12, 18, 30, 是], [12, 20, 32, 是], [12, 22, 34, 是], [12, 24, 36, 是], [12, 26, 38, 是], [12, 28, 40, 是], [12, 30, 42, 是], [12, 32, 44, 是], [12, 34, 0, 是], [12, 36, 2, 是], [12, 38, 4, 是], [12, 40, 6, 是], [12, 42, 8, 是], [12, 44, 10, 是], [14, 0, 14, 是], [14, 2, 16, 是], [14, 4, 18, 是], [14, 6, 20, 是], [14, 8, 22, 是], [14, 10, 24, 是], [14, 12, 26, 是], [14, 14, 28, 是], [14, 16, 30, 是], [14, 18, 32, 是], [14, 20, 34, 是], [14, 22, 36, 是], [14, 24, 38, 是], [14, 26, 40, 是], [14, 28, 42, 是], [14, 30, 44, 是], [14, 32, 0, 是], [14, 34, 2, 是], [14, 36, 4, 是], [14, 38, 6, 是], [14, 40, 8, 是], [14, 42, 10, 是], [14, 44, 12, 是], [16, 0, 16, 是], [16, 2, 18, 是], [16, 4, 20, 是], [16, 6, 22, 是], [16, 8, 24, 是], [16, 10, 26, 是], [16, 12, 28, 是], [16, 14, 30, 是], [16, 16, 32, 是], [16, 18, 34, 是], [16, 20, 36, 是], [16, 22, 38, 是], [16, 24, 40, 是], [16, 26, 42, 是], [16, 28, 44, 是], [16, 30, 0, 是], [16, 32, 2, 是], [16, 34, 4, 是], [16, 36, 6, 是], [16, 38, 8, 是], [16, 40, 10, 是], [16, 42, 12, 是], [16, 44, 14, 是], [18, 0, 18, 是], [18, 2, 20, 是], [18, 4, 22, 是], [18, 6, 24, 是], [18, 8, 26, 是], [18, 10, 28, 是], [18, 12, 30, 是], [18, 14, 32, 是], [18, 16, 34, 是], [18, 18, 36, 是], [18, 20, 38, 是], [18, 22, 40, 是], [18, 24, 42, 是], [18, 26, 44, 是], [18, 28, 0, 是], [18, 30, 2, 是], [18, 32, 4, 是], [18, 34, 6, 是], [18, 36, 8, 是], [18, 38, 10, 是], [18, 40, 12, 是], [18, 42, 14, 是], [18, 44, 16, 是], [20, 0, 20, 是], [20, 2, 22, 是], [20, 4, 24, 是], [20, 6, 26, 是], [20, 8, 28, 是], [20, 10, 30, 是], [20, 12, 32, 是], [20, 14, 34, 是], [20, 16, 36, 是], [20, 18, 38, 是], [20, 20, 40, 是], [20, 22, 42, 是], [20, 24, 44, 是], [20, 26, 0, 是], [20, 28, 2, 是], [20, 30, 4, 是], [20, 32, 6, 是], [20, 34, 8, 是], [20, 36, 10, 是], [20, 38, 12, 是], [20, 40, 14, 是], [20, 42, 16, 是], [20, 44, 18, 是], [22, 0, 22, 是], [22, 2, 24, 是], [22, 4, 26, 是], [22, 6, 28, 是], [22, 8, 30, 是], [22, 10, 32, 是], [22, 12, 34, 是], [22, 14, 36, 是], [22, 16, 38, 是], [22, 18, 40, 是], [22, 20, 42, 是], [22, 22, 44, 是], [22, 24, 0, 是], [22, 26, 2, 是], [22, 28, 4, 是], [22, 30, 6, 是], [22, 32, 8, 是], [22, 34, 10, 是], [22, 36, 12, 是], [22, 38, 14, 是], [22, 40, 16, 是], [22, 42, 18, 是], [22, 44, 20, 是], [24, 0, 24, 是], [24, 2, 26, 是], [24, 4, 28, 是], [24, 6, 30, 是], [24, 8, 32, 是], [24, 10, 34, 是], [24, 12, 36, 是], [24, 14, 38, 是], [24, 16, 40, 是], [24, 18, 42, 是], [24, 20, 44, 是], [24, 22, 0, 是], [24, 24, 2, 是], [24, 26, 4, 是], [24, 28, 6, 是], [24, 30, 8, 是], [24, 32, 10, 是], [24, 34, 12, 是], [24, 36, 14, 是], [24, 38, 16, 是], [24, 40, 18, 是], [24, 42, 20, 是], [24, 44, 22, 是], [26, 0, 26, 是], [26, 2, 28, 是], [26, 4, 30, 是], [26, 6, 32, 是], [26, 8, 34, 是], [26, 10, 36, 是], [26, 12, 38, 是], [26, 14, 40, 是], [26, 16, 42, 是], [26, 18, 44, 是], [26, 20, 0, 是], [26, 22, 2, 是], [26, 24, 4, 是], [26, 26, 6, 是], [26, 28, 8, 是], [26, 30, 10, 是], [26, 32, 12, 是], [26, 34, 14, 是], [26, 36, 16, 是], [26, 38, 18, 是], [26, 40, 20, 是], [26, 42, 22, 是], [26, 44, 24, 是], [28, 0, 28, 是], [28, 2, 30, 是], [28, 4, 32, 是], [28, 6, 34, 是], [28, 8, 36, 是], [28, 10, 38, 是], [28, 12, 40, 是], [28, 14, 42, 是], [28, 16, 44, 是], [28, 18, 0, 是], [28, 20, 2, 是], [28, 22, 4, 是], [28, 24, 6, 是], [28, 26, 8, 是], [28, 28, 10, 是], [28, 30, 12, 是], [28, 32, 14, 是], [28, 34, 16, 是], [28, 36, 18, 是], [28, 38, 20, 是], [28, 40, 22, 是], [28, 42, 24, 是], [28, 44, 26, 是], [30, 0, 30, 是], [30, 2, 32, 是], [30, 4, 34, 是], [30, 6, 36, 是], [30, 8, 38, 是], [30, 10, 40, 是], [30, 12, 42, 是], [30, 14, 44, 是], [30, 16, 0, 是], [30, 18, 2, 是], [30, 20, 4, 是], [30, 22, 6, 是], [30, 24, 8, 是], [30, 26, 10, 是], [30, 28, 12, 是], [30, 30, 14, 是], [30, 32, 16, 是], [30, 34, 18, 是], [30, 36, 20, 是], [30, 38, 22, 是], [30, 40, 24, 是], [30, 42, 26, 是], [30, 44, 28, 是], [32, 0, 32, 是], [32, 2, 34, 是], [32, 4, 36, 是], [32, 6, 38, 是], [32, 8, 40, 是], [32, 10, 42, 是], [32, 12, 44, 是], [32, 14, 0, 是], [32, 16, 2, 是], [32, 18, 4, 是], [32, 20, 6, 是], [32, 22, 8, 是], [32, 24, 10, 是], [32, 26, 12, 是], [32, 28, 14, 是], [32, 30, 16, 是], [32, 32, 18, 是], [32, 34, 20, 是], [32, 36, 22, 是], [32, 38, 24, 是], [32, 40, 26, 是], [32, 42, 28, 是], [32, 44, 30, 是], [34, 0, 34, 是], [34, 2, 36, 是], [34, 4, 38, 是], [34, 6, 40, 是], [34, 8, 42, 是], [34, 10, 44, 是], [34, 12, 0, 是], [34, 14, 2, 是], [34, 16, 4, 是], [34, 18, 6, 是], [34, 20, 8, 是], [34, 22, 10, 是], [34, 24, 12, 是], [34, 26, 14, 是], [34, 28, 16, 是], [34, 30, 18, 是], [34, 32, 20, 是], [34, 34, 22, 是], [34, 36, 24, 是], [34, 38, 26, 是], [34, 40, 28, 是], [34, 42, 30, 是], [34, 44, 32, 是], [36, 0, 36, 是], [36, 2, 38, 是], [36, 4, 40, 是], [36, 6, 42, 是], [36, 8, 44, 是], [36, 10, 0, 是], [36, 12, 2, 是], [36, 14, 4, 是], [36, 16, 6, 是], [36, 18, 8, 是], [36, 20, 10, 是], [36, 22, 12, 是], [36, 24, 14, 是], [36, 26, 16, 是], [36, 28, 18, 是], [36, 30, 20, 是], [36, 32, 22, 是], [36, 34, 24, 是], [36, 36, 26, 是], [36, 38, 28, 是], [36, 40, 30, 是], [36, 42, 32, 是], [36, 44, 34, 是], [38, 0, 38, 是], [38, 2, 40, 是], [38, 4, 42, 是], [38, 6, 44, 是], [38, 8, 0, 是], [38, 10, 2, 是], [38, 12, 4, 是], [38, 14, 6, 是], [38, 16, 8, 是], [38, 18, 10, 是], [38, 20, 12, 是], [38, 22, 14, 是], [38, 24, 16, 是], [38, 26, 18, 是], [38, 28, 20, 是], [38, 30, 22, 是], [38, 32, 24, 是], [38, 34, 26, 是], [38, 36, 28, 是], [38, 38, 30, 是], [38, 40, 32, 是], [38, 42, 34, 是], [38, 44, 36, 是], [40, 0, 40, 是], [40, 2, 42, 是], [40, 4, 44, 是], [40, 6, 0, 是], [40, 8, 2, 是], [40, 10, 4, 是], [40, 12, 6, 是], [40, 14, 8, 是], [40, 16, 10, 是], [40, 18, 12, 是], [40, 20, 14, 是], [40, 22, 16, 是], [40, 24, 18, 是], [40, 26, 20, 是], [40, 28, 22, 是], [40, 30, 24, 是], [40, 32, 26, 是], [40, 34, 28, 是], [40, 36, 30, 是], [40, 38, 32, 是], [40, 40, 34, 是], [40, 42, 36, 是], [40, 44, 38, 是], [42, 0, 42, 是], [42, 2, 44, 是], [42, 4, 0, 是], [42, 6, 2, 是], [42, 8, 4, 是], [42, 10, 6, 是], [42, 12, 8, 是], [42, 14, 10, 是], [42, 16, 12, 是], [42, 18, 14, 是], [42, 20, 16, 是], [42, 22, 18, 是], [42, 24, 20, 是], [42, 26, 22, 是], [42, 28, 24, 是], [42, 30, 26, 是], [42, 32, 28, 是], [42, 34, 30, 是], [42, 36, 32, 是], [42, 38, 34, 是], [42, 40, 36, 是], [42, 42, 38, 是], [42, 44, 40, 是], [44, 0, 44, 是], [44, 2, 0, 是], [44, 4, 2, 是], [44, 6, 4, 是], [44, 8, 6, 是], [44, 10, 8, 是], [44, 12, 10, 是], [44, 14, 12, 是], [44, 16, 14, 是], [44, 18, 16, 是], [44, 20, 18, 是], [44, 22, 20, 是], [44, 24, 22, 是], [44, 26, 24, 是], [44, 28, 26, 是], [44, 30, 28, 是], [44, 32, 30, 是], [44, 34, 32, 是], [44, 36, 34, 是], [44, 38, 36, 是], [44, 40, 38, 是], [44, 42, 40, 是], [44, 44, 42, 是]], 是, [[0, 0, 是], [2, 44, 是], [4, 42, 是], [6, 40, 是], [8, 38, 是], [10, 36, 是], [12, 34, 是], [14, 32, 是], [16, 30, 是], [18, 28, 是], [20, 26, 是], [22, 24, 是], [24, 22, 是], [26, 20, 是], [28, 18, 是], [30, 16, 是], [32, 14, 是], [34, 12, 是], [36, 10, 是], [38, 8, 是], [40, 6, 是], [42, 4, 是], [44, 2, 是]], 是, 是, [[0, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44], 是], [1, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44], 是], [2, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44], 是], [3, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44], 是], [4, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44], 是], [5, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44], 是], [6, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44], 是], [7, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44], 是], [8, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44], 是], [9, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44], 是], [10, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44], 是], [11, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44], 是], [12, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44], 是], [13, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44], 是], [14, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44], 是], [15, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44], 是], [16, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44], 是], [17, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44], 是], [18, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44], 是], [19, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44], 是], [20, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44], 是], [21, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44], 是], [22, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44], 是], [23, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44], 是], [24, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44], 是], [25, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44], 是], [26, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44], 是], [27, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44], 是], [28, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44], 是], [29, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44], 是], [30, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44], 是], [31, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44], 是], [32, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44], 是], [33, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44], 是], [34, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44], 是], [35, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44], 是], [36, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44], 是], [37, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44], 是], [38, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44], 是], [39, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44], 是], [40, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44], 是], [41, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44], 是], [42, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44], 是], [43, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44], 是], [44, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44], 是], [45, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44], 是]], 是] 條件：無 含identity、全部product與inverse closure各核，三者合取才成subgroup；再逐全部g驗normal。即使某map失敗，這些實際property仍可分別True，不由定理名稱填旗標。 步驟識別與依賴規則：Subgroup_actual_identity_product_inverse_ALL_conjugates · 依賴：G001, S006 S008 · implies操作前 source roles = [[0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44], 0, 0] 操作後 derived = [[[0, 0, 0, 0, 是], [0, 1, 2, 2, 是], [0, 2, 4, 4, 是], [0, 3, 6, 6, 是], [0, 4, 8, 8, 是], [0, 5, 10, 10, 是], [0, 6, 12, 12, 是], [0, 7, 14, 14, 是], [0, 8, 16, 16, 是], [0, 9, 18, 18, 是], [0, 10, 20, 20, 是], [0, 11, 22, 22, 是], [0, 12, 24, 24, 是], [0, 13, 26, 26, 是], [0, 14, 28, 28, 是], [0, 15, 30, 30, 是], [0, 16, 32, 32, 是], [0, 17, 34, 34, 是], [0, 18, 36, 36, 是], [0, 19, 38, 38, 是], [0, 20, 40, 40, 是], [0, 21, 42, 42, 是], [0, 22, 44, 44, 是], [1, 0, 2, 2, 是], [1, 1, 4, 4, 是], [1, 2, 6, 6, 是], [1, 3, 8, 8, 是], [1, 4, 10, 10, 是], [1, 5, 12, 12, 是], [1, 6, 14, 14, 是], [1, 7, 16, 16, 是], [1, 8, 18, 18, 是], [1, 9, 20, 20, 是], [1, 10, 22, 22, 是], [1, 11, 24, 24, 是], [1, 12, 26, 26, 是], [1, 13, 28, 28, 是], [1, 14, 30, 30, 是], [1, 15, 32, 32, 是], [1, 16, 34, 34, 是], [1, 17, 36, 36, 是], [1, 18, 38, 38, 是], [1, 19, 40, 40, 是], [1, 20, 42, 42, 是], [1, 21, 44, 44, 是], [1, 22, 0, 0, 是], [2, 0, 4, 4, 是], [2, 1, 6, 6, 是], [2, 2, 8, 8, 是], [2, 3, 10, 10, 是], [2, 4, 12, 12, 是], [2, 5, 14, 14, 是], [2, 6, 16, 16, 是], [2, 7, 18, 18, 是], [2, 8, 20, 20, 是], [2, 9, 22, 22, 是], [2, 10, 24, 24, 是], [2, 11, 26, 26, 是], [2, 12, 28, 28, 是], [2, 13, 30, 30, 是], [2, 14, 32, 32, 是], [2, 15, 34, 34, 是], [2, 16, 36, 36, 是], [2, 17, 38, 38, 是], [2, 18, 40, 40, 是], [2, 19, 42, 42, 是], [2, 20, 44, 44, 是], [2, 21, 0, 0, 是], [2, 22, 2, 2, 是], [3, 0, 6, 6, 是], [3, 1, 8, 8, 是], [3, 2, 10, 10, 是], [3, 3, 12, 12, 是], [3, 4, 14, 14, 是], [3, 5, 16, 16, 是], [3, 6, 18, 18, 是], [3, 7, 20, 20, 是], [3, 8, 22, 22, 是], [3, 9, 24, 24, 是], [3, 10, 26, 26, 是], [3, 11, 28, 28, 是], [3, 12, 30, 30, 是], [3, 13, 32, 32, 是], [3, 14, 34, 34, 是], [3, 15, 36, 36, 是], [3, 16, 38, 38, 是], [3, 17, 40, 40, 是], [3, 18, 42, 42, 是], [3, 19, 44, 44, 是], [3, 20, 0, 0, 是], [3, 21, 2, 2, 是], [3, 22, 4, 4, 是], [4, 0, 8, 8, 是], [4, 1, 10, 10, 是], [4, 2, 12, 12, 是], [4, 3, 14, 14, 是], [4, 4, 16, 16, 是], [4, 5, 18, 18, 是], [4, 6, 20, 20, 是], [4, 7, 22, 22, 是], [4, 8, 24, 24, 是], [4, 9, 26, 26, 是], [4, 10, 28, 28, 是], [4, 11, 30, 30, 是], [4, 12, 32, 32, 是], [4, 13, 34, 34, 是], [4, 14, 36, 36, 是], [4, 15, 38, 38, 是], [4, 16, 40, 40, 是], [4, 17, 42, 42, 是], [4, 18, 44, 44, 是], [4, 19, 0, 0, 是], [4, 20, 2, 2, 是], [4, 21, 4, 4, 是], [4, 22, 6, 6, 是], [5, 0, 10, 10, 是], [5, 1, 12, 12, 是], [5, 2, 14, 14, 是], [5, 3, 16, 16, 是], [5, 4, 18, 18, 是], [5, 5, 20, 20, 是], [5, 6, 22, 22, 是], [5, 7, 24, 24, 是], [5, 8, 26, 26, 是], [5, 9, 28, 28, 是], [5, 10, 30, 30, 是], [5, 11, 32, 32, 是], [5, 12, 34, 34, 是], [5, 13, 36, 36, 是], [5, 14, 38, 38, 是], [5, 15, 40, 40, 是], [5, 16, 42, 42, 是], [5, 17, 44, 44, 是], [5, 18, 0, 0, 是], [5, 19, 2, 2, 是], [5, 20, 4, 4, 是], [5, 21, 6, 6, 是], [5, 22, 8, 8, 是], [6, 0, 12, 12, 是], [6, 1, 14, 14, 是], [6, 2, 16, 16, 是], [6, 3, 18, 18, 是], [6, 4, 20, 20, 是], [6, 5, 22, 22, 是], [6, 6, 24, 24, 是], [6, 7, 26, 26, 是], [6, 8, 28, 28, 是], [6, 9, 30, 30, 是], [6, 10, 32, 32, 是], [6, 11, 34, 34, 是], [6, 12, 36, 36, 是], [6, 13, 38, 38, 是], [6, 14, 40, 40, 是], [6, 15, 42, 42, 是], [6, 16, 44, 44, 是], [6, 17, 0, 0, 是], [6, 18, 2, 2, 是], [6, 19, 4, 4, 是], [6, 20, 6, 6, 是], [6, 21, 8, 8, 是], [6, 22, 10, 10, 是], [7, 0, 14, 14, 是], [7, 1, 16, 16, 是], [7, 2, 18, 18, 是], [7, 3, 20, 20, 是], [7, 4, 22, 22, 是], [7, 5, 24, 24, 是], [7, 6, 26, 26, 是], [7, 7, 28, 28, 是], [7, 8, 30, 30, 是], [7, 9, 32, 32, 是], [7, 10, 34, 34, 是], [7, 11, 36, 36, 是], [7, 12, 38, 38, 是], [7, 13, 40, 40, 是], [7, 14, 42, 42, 是], [7, 15, 44, 44, 是], [7, 16, 0, 0, 是], [7, 17, 2, 2, 是], [7, 18, 4, 4, 是], [7, 19, 6, 6, 是], [7, 20, 8, 8, 是], [7, 21, 10, 10, 是], [7, 22, 12, 12, 是], [8, 0, 16, 16, 是], [8, 1, 18, 18, 是], [8, 2, 20, 20, 是], [8, 3, 22, 22, 是], [8, 4, 24, 24, 是], [8, 5, 26, 26, 是], [8, 6, 28, 28, 是], [8, 7, 30, 30, 是], [8, 8, 32, 32, 是], [8, 9, 34, 34, 是], [8, 10, 36, 36, 是], [8, 11, 38, 38, 是], [8, 12, 40, 40, 是], [8, 13, 42, 42, 是], [8, 14, 44, 44, 是], [8, 15, 0, 0, 是], [8, 16, 2, 2, 是], [8, 17, 4, 4, 是], [8, 18, 6, 6, 是], [8, 19, 8, 8, 是], [8, 20, 10, 10, 是], [8, 21, 12, 12, 是], [8, 22, 14, 14, 是], [9, 0, 18, 18, 是], [9, 1, 20, 20, 是], [9, 2, 22, 22, 是], [9, 3, 24, 24, 是], [9, 4, 26, 26, 是], [9, 5, 28, 28, 是], [9, 6, 30, 30, 是], [9, 7, 32, 32, 是], [9, 8, 34, 34, 是], [9, 9, 36, 36, 是], [9, 10, 38, 38, 是], [9, 11, 40, 40, 是], [9, 12, 42, 42, 是], [9, 13, 44, 44, 是], [9, 14, 0, 0, 是], [9, 15, 2, 2, 是], [9, 16, 4, 4, 是], [9, 17, 6, 6, 是], [9, 18, 8, 8, 是], [9, 19, 10, 10, 是], [9, 20, 12, 12, 是], [9, 21, 14, 14, 是], [9, 22, 16, 16, 是], [10, 0, 20, 20, 是], [10, 1, 22, 22, 是], [10, 2, 24, 24, 是], [10, 3, 26, 26, 是], [10, 4, 28, 28, 是], [10, 5, 30, 30, 是], [10, 6, 32, 32, 是], [10, 7, 34, 34, 是], [10, 8, 36, 36, 是], [10, 9, 38, 38, 是], [10, 10, 40, 40, 是], [10, 11, 42, 42, 是], [10, 12, 44, 44, 是], [10, 13, 0, 0, 是], [10, 14, 2, 2, 是], [10, 15, 4, 4, 是], [10, 16, 6, 6, 是], [10, 17, 8, 8, 是], [10, 18, 10, 10, 是], [10, 19, 12, 12, 是], [10, 20, 14, 14, 是], [10, 21, 16, 16, 是], [10, 22, 18, 18, 是], [11, 0, 22, 22, 是], [11, 1, 24, 24, 是], [11, 2, 26, 26, 是], [11, 3, 28, 28, 是], [11, 4, 30, 30, 是], [11, 5, 32, 32, 是], [11, 6, 34, 34, 是], [11, 7, 36, 36, 是], [11, 8, 38, 38, 是], [11, 9, 40, 40, 是], [11, 10, 42, 42, 是], [11, 11, 44, 44, 是], [11, 12, 0, 0, 是], [11, 13, 2, 2, 是], [11, 14, 4, 4, 是], [11, 15, 6, 6, 是], [11, 16, 8, 8, 是], [11, 17, 10, 10, 是], [11, 18, 12, 12, 是], [11, 19, 14, 14, 是], [11, 20, 16, 16, 是], [11, 21, 18, 18, 是], [11, 22, 20, 20, 是], [12, 0, 24, 24, 是], [12, 1, 26, 26, 是], [12, 2, 28, 28, 是], [12, 3, 30, 30, 是], [12, 4, 32, 32, 是], [12, 5, 34, 34, 是], [12, 6, 36, 36, 是], [12, 7, 38, 38, 是], [12, 8, 40, 40, 是], [12, 9, 42, 42, 是], [12, 10, 44, 44, 是], [12, 11, 0, 0, 是], [12, 12, 2, 2, 是], [12, 13, 4, 4, 是], [12, 14, 6, 6, 是], [12, 15, 8, 8, 是], [12, 16, 10, 10, 是], [12, 17, 12, 12, 是], [12, 18, 14, 14, 是], [12, 19, 16, 16, 是], [12, 20, 18, 18, 是], [12, 21, 20, 20, 是], [12, 22, 22, 22, 是], [13, 0, 26, 26, 是], [13, 1, 28, 28, 是], [13, 2, 30, 30, 是], [13, 3, 32, 32, 是], [13, 4, 34, 34, 是], [13, 5, 36, 36, 是], [13, 6, 38, 38, 是], [13, 7, 40, 40, 是], [13, 8, 42, 42, 是], [13, 9, 44, 44, 是], [13, 10, 0, 0, 是], [13, 11, 2, 2, 是], [13, 12, 4, 4, 是], [13, 13, 6, 6, 是], [13, 14, 8, 8, 是], [13, 15, 10, 10, 是], [13, 16, 12, 12, 是], [13, 17, 14, 14, 是], [13, 18, 16, 16, 是], [13, 19, 18, 18, 是], [13, 20, 20, 20, 是], [13, 21, 22, 22, 是], [13, 22, 24, 24, 是], [14, 0, 28, 28, 是], [14, 1, 30, 30, 是], [14, 2, 32, 32, 是], [14, 3, 34, 34, 是], [14, 4, 36, 36, 是], [14, 5, 38, 38, 是], [14, 6, 40, 40, 是], [14, 7, 42, 42, 是], [14, 8, 44, 44, 是], [14, 9, 0, 0, 是], [14, 10, 2, 2, 是], [14, 11, 4, 4, 是], [14, 12, 6, 6, 是], [14, 13, 8, 8, 是], [14, 14, 10, 10, 是], [14, 15, 12, 12, 是], [14, 16, 14, 14, 是], [14, 17, 16, 16, 是], [14, 18, 18, 18, 是], [14, 19, 20, 20, 是], [14, 20, 22, 22, 是], [14, 21, 24, 24, 是], [14, 22, 26, 26, 是], [15, 0, 30, 30, 是], [15, 1, 32, 32, 是], [15, 2, 34, 34, 是], [15, 3, 36, 36, 是], [15, 4, 38, 38, 是], [15, 5, 40, 40, 是], [15, 6, 42, 42, 是], [15, 7, 44, 44, 是], [15, 8, 0, 0, 是], [15, 9, 2, 2, 是], [15, 10, 4, 4, 是], [15, 11, 6, 6, 是], [15, 12, 8, 8, 是], [15, 13, 10, 10, 是], [15, 14, 12, 12, 是], [15, 15, 14, 14, 是], [15, 16, 16, 16, 是], [15, 17, 18, 18, 是], [15, 18, 20, 20, 是], [15, 19, 22, 22, 是], [15, 20, 24, 24, 是], [15, 21, 26, 26, 是], [15, 22, 28, 28, 是], [16, 0, 32, 32, 是], [16, 1, 34, 34, 是], [16, 2, 36, 36, 是], [16, 3, 38, 38, 是], [16, 4, 40, 40, 是], [16, 5, 42, 42, 是], [16, 6, 44, 44, 是], [16, 7, 0, 0, 是], [16, 8, 2, 2, 是], [16, 9, 4, 4, 是], [16, 10, 6, 6, 是], [16, 11, 8, 8, 是], [16, 12, 10, 10, 是], [16, 13, 12, 12, 是], [16, 14, 14, 14, 是], [16, 15, 16, 16, 是], [16, 16, 18, 18, 是], [16, 17, 20, 20, 是], [16, 18, 22, 22, 是], [16, 19, 24, 24, 是], [16, 20, 26, 26, 是], [16, 21, 28, 28, 是], [16, 22, 30, 30, 是], [17, 0, 34, 34, 是], [17, 1, 36, 36, 是], [17, 2, 38, 38, 是], [17, 3, 40, 40, 是], [17, 4, 42, 42, 是], [17, 5, 44, 44, 是], [17, 6, 0, 0, 是], [17, 7, 2, 2, 是], [17, 8, 4, 4, 是], [17, 9, 6, 6, 是], [17, 10, 8, 8, 是], [17, 11, 10, 10, 是], [17, 12, 12, 12, 是], [17, 13, 14, 14, 是], [17, 14, 16, 16, 是], [17, 15, 18, 18, 是], [17, 16, 20, 20, 是], [17, 17, 22, 22, 是], [17, 18, 24, 24, 是], [17, 19, 26, 26, 是], [17, 20, 28, 28, 是], [17, 21, 30, 30, 是], [17, 22, 32, 32, 是], [18, 0, 36, 36, 是], [18, 1, 38, 38, 是], [18, 2, 40, 40, 是], [18, 3, 42, 42, 是], [18, 4, 44, 44, 是], [18, 5, 0, 0, 是], [18, 6, 2, 2, 是], [18, 7, 4, 4, 是], [18, 8, 6, 6, 是], [18, 9, 8, 8, 是], [18, 10, 10, 10, 是], [18, 11, 12, 12, 是], [18, 12, 14, 14, 是], [18, 13, 16, 16, 是], [18, 14, 18, 18, 是], [18, 15, 20, 20, 是], [18, 16, 22, 22, 是], [18, 17, 24, 24, 是], [18, 18, 26, 26, 是], [18, 19, 28, 28, 是], [18, 20, 30, 30, 是], [18, 21, 32, 32, 是], [18, 22, 34, 34, 是], [19, 0, 38, 38, 是], [19, 1, 40, 40, 是], [19, 2, 42, 42, 是], [19, 3, 44, 44, 是], [19, 4, 0, 0, 是], [19, 5, 2, 2, 是], [19, 6, 4, 4, 是], [19, 7, 6, 6, 是], [19, 8, 8, 8, 是], [19, 9, 10, 10, 是], [19, 10, 12, 12, 是], [19, 11, 14, 14, 是], [19, 12, 16, 16, 是], [19, 13, 18, 18, 是], [19, 14, 20, 20, 是], [19, 15, 22, 22, 是], [19, 16, 24, 24, 是], [19, 17, 26, 26, 是], [19, 18, 28, 28, 是], [19, 19, 30, 30, 是], [19, 20, 32, 32, 是], [19, 21, 34, 34, 是], [19, 22, 36, 36, 是], [20, 0, 40, 40, 是], [20, 1, 42, 42, 是], [20, 2, 44, 44, 是], [20, 3, 0, 0, 是], [20, 4, 2, 2, 是], [20, 5, 4, 4, 是], [20, 6, 6, 6, 是], [20, 7, 8, 8, 是], [20, 8, 10, 10, 是], [20, 9, 12, 12, 是], [20, 10, 14, 14, 是], [20, 11, 16, 16, 是], [20, 12, 18, 18, 是], [20, 13, 20, 20, 是], [20, 14, 22, 22, 是], [20, 15, 24, 24, 是], [20, 16, 26, 26, 是], [20, 17, 28, 28, 是], [20, 18, 30, 30, 是], [20, 19, 32, 32, 是], [20, 20, 34, 34, 是], [20, 21, 36, 36, 是], [20, 22, 38, 38, 是], [21, 0, 42, 42, 是], [21, 1, 44, 44, 是], [21, 2, 0, 0, 是], [21, 3, 2, 2, 是], [21, 4, 4, 4, 是], [21, 5, 6, 6, 是], [21, 6, 8, 8, 是], [21, 7, 10, 10, 是], [21, 8, 12, 12, 是], [21, 9, 14, 14, 是], [21, 10, 16, 16, 是], [21, 11, 18, 18, 是], [21, 12, 20, 20, 是], [21, 13, 22, 22, 是], [21, 14, 24, 24, 是], [21, 15, 26, 26, 是], [21, 16, 28, 28, 是], [21, 17, 30, 30, 是], [21, 18, 32, 32, 是], [21, 19, 34, 34, 是], [21, 20, 36, 36, 是], [21, 21, 38, 38, 是], [21, 22, 40, 40, 是], [22, 0, 44, 44, 是], [22, 1, 0, 0, 是], [22, 2, 2, 2, 是], [22, 3, 4, 4, 是], [22, 4, 6, 6, 是], [22, 5, 8, 8, 是], [22, 6, 10, 10, 是], [22, 7, 12, 12, 是], [22, 8, 14, 14, 是], [22, 9, 16, 16, 是], [22, 10, 18, 18, 是], [22, 11, 20, 20, 是], [22, 12, 22, 22, 是], [22, 13, 24, 24, 是], [22, 14, 26, 26, 是], [22, 15, 28, 28, 是], [22, 16, 30, 30, 是], [22, 17, 32, 32, 是], [22, 18, 34, 34, 是], [22, 19, 36, 36, 是], [22, 20, 38, 38, 是], [22, 21, 40, 40, 是], [22, 22, 42, 42, 是]], 是, null, [0], [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44], 是, 是] 條件：無 全pair驗同態，並取完整target identity preimage與image。qualification允許bad map且property按實際核，可能同態False而kernel normal／image subgroup True；空kernel不補identity fallback。 步驟識別與依賴規則：Iso1_ALL_product_laws_ACTUAL_kernel_image_properties_before_theorem · 依賴：G001, S007 S009 · implies操作前 source roles = [[0], 是, [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44]] 操作後 derived = [[[0], [1], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [2], [20], [21], [22], [3], [4], [5], [6], [7], [8], [9]], [0, 1, 12, 16, 17, 18, 19, 20, 21, 22, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15], [[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22], [1, 12, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 16, 14, 15, 0, 17, 18, 19, 20, 21, 22, 2], [2, 3, 13, 14, 15, 0, 1, 12, 16, 17, 18, 19, 4, 20, 21, 22, 5, 6, 7, 8, 9, 10, 11], [3, 4, 14, 15, 0, 1, 12, 16, 17, 18, 19, 20, 5, 21, 22, 2, 6, 7, 8, 9, 10, 11, 13], [4, 5, 15, 0, 1, 12, 16, 17, 18, 19, 20, 21, 6, 22, 2, 3, 7, 8, 9, 10, 11, 13, 14], [5, 6, 0, 1, 12, 16, 17, 18, 19, 20, 21, 22, 7, 2, 3, 4, 8, 9, 10, 11, 13, 14, 15], [6, 7, 1, 12, 16, 17, 18, 19, 20, 21, 22, 2, 8, 3, 4, 5, 9, 10, 11, 13, 14, 15, 0], [7, 8, 12, 16, 17, 18, 19, 20, 21, 22, 2, 3, 9, 4, 5, 6, 10, 11, 13, 14, 15, 0, 1], [8, 9, 16, 17, 18, 19, 20, 21, 22, 2, 3, 4, 10, 5, 6, 7, 11, 13, 14, 15, 0, 1, 12], [9, 10, 17, 18, 19, 20, 21, 22, 2, 3, 4, 5, 11, 6, 7, 8, 13, 14, 15, 0, 1, 12, 16], [10, 11, 18, 19, 20, 21, 22, 2, 3, 4, 5, 6, 13, 7, 8, 9, 14, 15, 0, 1, 12, 16, 17], [11, 13, 19, 20, 21, 22, 2, 3, 4, 5, 6, 7, 14, 8, 9, 10, 15, 0, 1, 12, 16, 17, 18], [12, 16, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 17, 15, 0, 1, 18, 19, 20, 21, 22, 2, 3], [13, 14, 20, 21, 22, 2, 3, 4, 5, 6, 7, 8, 15, 9, 10, 11, 0, 1, 12, 16, 17, 18, 19], [14, 15, 21, 22, 2, 3, 4, 5, 6, 7, 8, 9, 0, 10, 11, 13, 1, 12, 16, 17, 18, 19, 20], [15, 0, 22, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 11, 13, 14, 12, 16, 17, 18, 19, 20, 21], [16, 17, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 18, 0, 1, 12, 19, 20, 21, 22, 2, 3, 4], [17, 18, 6, 7, 8, 9, 10, 11, 13, 14, 15, 0, 19, 1, 12, 16, 20, 21, 22, 2, 3, 4, 5], [18, 19, 7, 8, 9, 10, 11, 13, 14, 15, 0, 1, 20, 12, 16, 17, 21, 22, 2, 3, 4, 5, 6], [19, 20, 8, 9, 10, 11, 13, 14, 15, 0, 1, 12, 21, 16, 17, 18, 22, 2, 3, 4, 5, 6, 7], [20, 21, 9, 10, 11, 13, 14, 15, 0, 1, 12, 16, 22, 17, 18, 19, 2, 3, 4, 5, 6, 7, 8], [21, 22, 10, 11, 13, 14, 15, 0, 1, 12, 16, 17, 2, 18, 19, 20, 3, 4, 5, 6, 7, 8, 9], [22, 2, 11, 13, 14, 15, 0, 1, 12, 16, 17, 18, 3, 19, 20, 21, 4, 5, 6, 7, 8, 9, 10]], [[0, 0, [0], 是], [0, 1, [1], 是], [0, 2, [2], 是], [0, 3, [3], 是], [0, 4, [4], 是], [0, 5, [5], 是], [0, 6, [6], 是], [0, 7, [7], 是], [0, 8, [8], 是], [0, 9, [9], 是], [0, 10, [10], 是], [0, 11, [11], 是], [0, 12, [12], 是], [0, 13, [13], 是], [0, 14, [14], 是], [0, 15, [15], 是], [0, 16, [16], 是], [0, 17, [17], 是], [0, 18, [18], 是], [0, 19, [19], 是], [0, 20, [20], 是], [0, 21, [21], 是], [0, 22, [22], 是], [1, 0, [1], 是], [1, 1, [12], 是], [1, 2, [3], 是], [1, 3, [4], 是], [1, 4, [5], 是], [1, 5, [6], 是], [1, 6, [7], 是], [1, 7, [8], 是], [1, 8, [9], 是], [1, 9, [10], 是], [1, 10, [11], 是], [1, 11, [13], 是], [1, 12, [16], 是], [1, 13, [14], 是], [1, 14, [15], 是], [1, 15, [0], 是], [1, 16, [17], 是], [1, 17, [18], 是], [1, 18, [19], 是], [1, 19, [20], 是], [1, 20, [21], 是], [1, 21, [22], 是], [1, 22, [2], 是], [2, 0, [2], 是], [2, 1, [3], 是], [2, 2, [13], 是], [2, 3, [14], 是], [2, 4, [15], 是], [2, 5, [0], 是], [2, 6, [1], 是], [2, 7, [12], 是], [2, 8, [16], 是], [2, 9, [17], 是], [2, 10, [18], 是], [2, 11, [19], 是], [2, 12, [4], 是], [2, 13, [20], 是], [2, 14, [21], 是], [2, 15, [22], 是], [2, 16, [5], 是], [2, 17, [6], 是], [2, 18, [7], 是], [2, 19, [8], 是], [2, 20, [9], 是], [2, 21, [10], 是], [2, 22, [11], 是], [3, 0, [3], 是], [3, 1, [4], 是], [3, 2, [14], 是], [3, 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是], [20, 7, [15], 是], [20, 8, [0], 是], [20, 9, [1], 是], [20, 10, [12], 是], [20, 11, [16], 是], [20, 12, [22], 是], [20, 13, [17], 是], [20, 14, [18], 是], [20, 15, [19], 是], [20, 16, [2], 是], [20, 17, [3], 是], [20, 18, [4], 是], [20, 19, [5], 是], [20, 20, [6], 是], [20, 21, [7], 是], [20, 22, [8], 是], [21, 0, [21], 是], [21, 1, [22], 是], [21, 2, [10], 是], [21, 3, [11], 是], [21, 4, [13], 是], [21, 5, [14], 是], [21, 6, [15], 是], [21, 7, [0], 是], [21, 8, [1], 是], [21, 9, [12], 是], [21, 10, [16], 是], [21, 11, [17], 是], [21, 12, [2], 是], [21, 13, [18], 是], [21, 14, [19], 是], [21, 15, [20], 是], [21, 16, [3], 是], [21, 17, [4], 是], [21, 18, [5], 是], [21, 19, [6], 是], [21, 20, [7], 是], [21, 21, [8], 是], [21, 22, [9], 是], [22, 0, [22], 是], [22, 1, [2], 是], [22, 2, [11], 是], [22, 3, [13], 是], [22, 4, [14], 是], [22, 5, [15], 是], [22, 6, [0], 是], [22, 7, [1], 是], [22, 8, [12], 是], [22, 9, [16], 是], [22, 10, [17], 是], [22, 11, [18], 是], [22, 12, [3], 是], [22, 13, [19], 是], [22, 14, [20], 是], [22, 15, [21], 是], [22, 16, [4], 是], [22, 17, [5], 是], [22, 18, [6], 是], [22, 19, [7], 是], [22, 20, [8], 是], [22, 21, [9], 是], [22, 22, [10], 是]], [[0, [0], [0], 是], [1, [1], [2], 是], [2, [10], [20], 是], [3, [11], [22], 是], [4, [12], [24], 是], [5, [13], [26], 是], [6, [14], [28], 是], [7, [15], [30], 是], [8, [16], [32], 是], [9, [17], [34], 是], [10, [18], [36], 是], [11, [19], [38], 是], [12, [2], [4], 是], [13, [20], [40], 是], [14, [21], [42], 是], [15, [22], [44], 是], [16, [3], [6], 是], [17, [4], [8], 是], [18, [5], [10], 是], [19, [6], [12], 是], [20, [7], [14], 是], [21, [8], [16], 是], [22, [9], [18], 是]], 是] 條件：無 kernel normal使(ah)(bk)=ab(b^-1hb)k∈abK，逐全部代表元驗product coset相同；同一coset的每個f(g)也須同值才定義bar_f。carrier是coset SETS而非首代表元。 步驟識別與依賴規則：Iso1_full_LEFT_coset_quotient_ALL_products_and_representative_images · 依賴：G001, S008 S010 · implies操作前 source roles = [[[0], [1], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [2], [20], [21], [22], [3], [4], [5], [6], [7], [8], [9]], [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44], [0, 2, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 4, 40, 42, 44, 6, 8, 10, 12, 14, 16, 18]] 操作後 derived = [[[0, 0, 0, 0, 是], [0, 1, 2, 2, 是], [0, 2, 20, 20, 是], [0, 3, 22, 22, 是], [0, 4, 24, 24, 是], [0, 5, 26, 26, 是], [0, 6, 28, 28, 是], [0, 7, 30, 30, 是], [0, 8, 32, 32, 是], [0, 9, 34, 34, 是], [0, 10, 36, 36, 是], [0, 11, 38, 38, 是], [0, 12, 4, 4, 是], [0, 13, 40, 40, 是], [0, 14, 42, 42, 是], [0, 15, 44, 44, 是], [0, 16, 6, 6, 是], [0, 17, 8, 8, 是], [0, 18, 10, 10, 是], [0, 19, 12, 12, 是], [0, 20, 14, 14, 是], [0, 21, 16, 16, 是], [0, 22, 18, 18, 是], [1, 0, 2, 2, 是], [1, 1, 4, 4, 是], [1, 2, 22, 22, 是], [1, 3, 24, 24, 是], [1, 4, 26, 26, 是], [1, 5, 28, 28, 是], [1, 6, 30, 30, 是], [1, 7, 32, 32, 是], [1, 8, 34, 34, 是], [1, 9, 36, 36, 是], [1, 10, 38, 38, 是], [1, 11, 40, 40, 是], [1, 12, 6, 6, 是], [1, 13, 42, 42, 是], [1, 14, 44, 44, 是], [1, 15, 0, 0, 是], [1, 16, 8, 8, 是], [1, 17, 10, 10, 是], [1, 18, 12, 12, 是], [1, 19, 14, 14, 是], [1, 20, 16, 16, 是], [1, 21, 18, 18, 是], [1, 22, 20, 20, 是], [2, 0, 20, 20, 是], [2, 1, 22, 22, 是], [2, 2, 40, 40, 是], [2, 3, 42, 42, 是], [2, 4, 44, 44, 是], [2, 5, 0, 0, 是], [2, 6, 2, 2, 是], [2, 7, 4, 4, 是], [2, 8, 6, 6, 是], [2, 9, 8, 8, 是], [2, 10, 10, 10, 是], [2, 11, 12, 12, 是], [2, 12, 24, 24, 是], [2, 13, 14, 14, 是], [2, 14, 16, 16, 是], [2, 15, 18, 18, 是], [2, 16, 26, 26, 是], [2, 17, 28, 28, 是], [2, 18, 30, 30, 是], [2, 19, 32, 32, 是], [2, 20, 34, 34, 是], [2, 21, 36, 36, 是], [2, 22, 38, 38, 是], [3, 0, 22, 22, 是], [3, 1, 24, 24, 是], [3, 2, 42, 42, 是], [3, 3, 44, 44, 是], [3, 4, 0, 0, 是], [3, 5, 2, 2, 是], [3, 6, 4, 4, 是], [3, 7, 6, 6, 是], [3, 8, 8, 8, 是], [3, 9, 10, 10, 是], [3, 10, 12, 12, 是], [3, 11, 14, 14, 是], [3, 12, 26, 26, 是], [3, 13, 16, 16, 是], [3, 14, 18, 18, 是], [3, 15, 20, 20, 是], [3, 16, 28, 28, 是], [3, 17, 30, 30, 是], [3, 18, 32, 32, 是], [3, 19, 34, 34, 是], [3, 20, 36, 36, 是], [3, 21, 38, 38, 是], [3, 22, 40, 40, 是], [4, 0, 24, 24, 是], [4, 1, 26, 26, 是], [4, 2, 44, 44, 是], [4, 3, 0, 0, 是], [4, 4, 2, 2, 是], [4, 5, 4, 4, 是], [4, 6, 6, 6, 是], [4, 7, 8, 8, 是], [4, 8, 10, 10, 是], [4, 9, 12, 12, 是], [4, 10, 14, 14, 是], [4, 11, 16, 16, 是], [4, 12, 28, 28, 是], [4, 13, 18, 18, 是], [4, 14, 20, 20, 是], [4, 15, 22, 22, 是], [4, 16, 30, 30, 是], [4, 17, 32, 32, 是], [4, 18, 34, 34, 是], [4, 19, 36, 36, 是], [4, 20, 38, 38, 是], [4, 21, 40, 40, 是], [4, 22, 42, 42, 是], [5, 0, 26, 26, 是], [5, 1, 28, 28, 是], [5, 2, 0, 0, 是], [5, 3, 2, 2, 是], [5, 4, 4, 4, 是], [5, 5, 6, 6, 是], [5, 6, 8, 8, 是], [5, 7, 10, 10, 是], [5, 8, 12, 12, 是], [5, 9, 14, 14, 是], [5, 10, 16, 16, 是], [5, 11, 18, 18, 是], [5, 12, 30, 30, 是], [5, 13, 20, 20, 是], [5, 14, 22, 22, 是], [5, 15, 24, 24, 是], [5, 16, 32, 32, 是], [5, 17, 34, 34, 是], [5, 18, 36, 36, 是], [5, 19, 38, 38, 是], [5, 20, 40, 40, 是], [5, 21, 42, 42, 是], [5, 22, 44, 44, 是], [6, 0, 28, 28, 是], [6, 1, 30, 30, 是], [6, 2, 2, 2, 是], [6, 3, 4, 4, 是], [6, 4, 6, 6, 是], [6, 5, 8, 8, 是], [6, 6, 10, 10, 是], [6, 7, 12, 12, 是], [6, 8, 14, 14, 是], [6, 9, 16, 16, 是], [6, 10, 18, 18, 是], [6, 11, 20, 20, 是], [6, 12, 32, 32, 是], [6, 13, 22, 22, 是], [6, 14, 24, 24, 是], [6, 15, 26, 26, 是], [6, 16, 34, 34, 是], [6, 17, 36, 36, 是], [6, 18, 38, 38, 是], [6, 19, 40, 40, 是], [6, 20, 42, 42, 是], [6, 21, 44, 44, 是], [6, 22, 0, 0, 是], [7, 0, 30, 30, 是], [7, 1, 32, 32, 是], [7, 2, 4, 4, 是], [7, 3, 6, 6, 是], [7, 4, 8, 8, 是], [7, 5, 10, 10, 是], [7, 6, 12, 12, 是], [7, 7, 14, 14, 是], [7, 8, 16, 16, 是], [7, 9, 18, 18, 是], [7, 10, 20, 20, 是], [7, 11, 22, 22, 是], [7, 12, 34, 34, 是], [7, 13, 24, 24, 是], [7, 14, 26, 26, 是], [7, 15, 28, 28, 是], [7, 16, 36, 36, 是], [7, 17, 38, 38, 是], [7, 18, 40, 40, 是], [7, 19, 42, 42, 是], [7, 20, 44, 44, 是], [7, 21, 0, 0, 是], [7, 22, 2, 2, 是], [8, 0, 32, 32, 是], [8, 1, 34, 34, 是], [8, 2, 6, 6, 是], [8, 3, 8, 8, 是], [8, 4, 10, 10, 是], [8, 5, 12, 12, 是], [8, 6, 14, 14, 是], [8, 7, 16, 16, 是], [8, 8, 18, 18, 是], [8, 9, 20, 20, 是], [8, 10, 22, 22, 是], [8, 11, 24, 24, 是], [8, 12, 36, 36, 是], [8, 13, 26, 26, 是], [8, 14, 28, 28, 是], [8, 15, 30, 30, 是], [8, 16, 38, 38, 是], [8, 17, 40, 40, 是], [8, 18, 42, 42, 是], [8, 19, 44, 44, 是], [8, 20, 0, 0, 是], [8, 21, 2, 2, 是], [8, 22, 4, 4, 是], [9, 0, 34, 34, 是], [9, 1, 36, 36, 是], [9, 2, 8, 8, 是], [9, 3, 10, 10, 是], [9, 4, 12, 12, 是], [9, 5, 14, 14, 是], [9, 6, 16, 16, 是], [9, 7, 18, 18, 是], [9, 8, 20, 20, 是], [9, 9, 22, 22, 是], [9, 10, 24, 24, 是], [9, 11, 26, 26, 是], [9, 12, 38, 38, 是], [9, 13, 28, 28, 是], [9, 14, 30, 30, 是], [9, 15, 32, 32, 是], [9, 16, 40, 40, 是], [9, 17, 42, 42, 是], [9, 18, 44, 44, 是], [9, 19, 0, 0, 是], [9, 20, 2, 2, 是], [9, 21, 4, 4, 是], [9, 22, 6, 6, 是], [10, 0, 36, 36, 是], [10, 1, 38, 38, 是], [10, 2, 10, 10, 是], [10, 3, 12, 12, 是], [10, 4, 14, 14, 是], [10, 5, 16, 16, 是], [10, 6, 18, 18, 是], [10, 7, 20, 20, 是], [10, 8, 22, 22, 是], [10, 9, 24, 24, 是], [10, 10, 26, 26, 是], [10, 11, 28, 28, 是], [10, 12, 40, 40, 是], [10, 13, 30, 30, 是], [10, 14, 32, 32, 是], [10, 15, 34, 34, 是], [10, 16, 42, 42, 是], [10, 17, 44, 44, 是], [10, 18, 0, 0, 是], [10, 19, 2, 2, 是], [10, 20, 4, 4, 是], [10, 21, 6, 6, 是], [10, 22, 8, 8, 是], [11, 0, 38, 38, 是], [11, 1, 40, 40, 是], [11, 2, 12, 12, 是], [11, 3, 14, 14, 是], [11, 4, 16, 16, 是], [11, 5, 18, 18, 是], [11, 6, 20, 20, 是], [11, 7, 22, 22, 是], [11, 8, 24, 24, 是], [11, 9, 26, 26, 是], [11, 10, 28, 28, 是], [11, 11, 30, 30, 是], [11, 12, 42, 42, 是], [11, 13, 32, 32, 是], [11, 14, 34, 34, 是], [11, 15, 36, 36, 是], [11, 16, 44, 44, 是], [11, 17, 0, 0, 是], [11, 18, 2, 2, 是], [11, 19, 4, 4, 是], [11, 20, 6, 6, 是], [11, 21, 8, 8, 是], [11, 22, 10, 10, 是], [12, 0, 4, 4, 是], [12, 1, 6, 6, 是], [12, 2, 24, 24, 是], [12, 3, 26, 26, 是], [12, 4, 28, 28, 是], [12, 5, 30, 30, 是], [12, 6, 32, 32, 是], [12, 7, 34, 34, 是], [12, 8, 36, 36, 是], [12, 9, 38, 38, 是], [12, 10, 40, 40, 是], [12, 11, 42, 42, 是], [12, 12, 8, 8, 是], [12, 13, 44, 44, 是], [12, 14, 0, 0, 是], [12, 15, 2, 2, 是], [12, 16, 10, 10, 是], [12, 17, 12, 12, 是], [12, 18, 14, 14, 是], [12, 19, 16, 16, 是], [12, 20, 18, 18, 是], [12, 21, 20, 20, 是], [12, 22, 22, 22, 是], [13, 0, 40, 40, 是], [13, 1, 42, 42, 是], [13, 2, 14, 14, 是], [13, 3, 16, 16, 是], [13, 4, 18, 18, 是], [13, 5, 20, 20, 是], [13, 6, 22, 22, 是], [13, 7, 24, 24, 是], [13, 8, 26, 26, 是], [13, 9, 28, 28, 是], [13, 10, 30, 30, 是], [13, 11, 32, 32, 是], [13, 12, 44, 44, 是], [13, 13, 34, 34, 是], [13, 14, 36, 36, 是], [13, 15, 38, 38, 是], [13, 16, 0, 0, 是], [13, 17, 2, 2, 是], [13, 18, 4, 4, 是], [13, 19, 6, 6, 是], [13, 20, 8, 8, 是], [13, 21, 10, 10, 是], [13, 22, 12, 12, 是], [14, 0, 42, 42, 是], [14, 1, 44, 44, 是], [14, 2, 16, 16, 是], [14, 3, 18, 18, 是], [14, 4, 20, 20, 是], [14, 5, 22, 22, 是], [14, 6, 24, 24, 是], [14, 7, 26, 26, 是], [14, 8, 28, 28, 是], [14, 9, 30, 30, 是], [14, 10, 32, 32, 是], [14, 11, 34, 34, 是], [14, 12, 0, 0, 是], [14, 13, 36, 36, 是], [14, 14, 38, 38, 是], [14, 15, 40, 40, 是], [14, 16, 2, 2, 是], [14, 17, 4, 4, 是], [14, 18, 6, 6, 是], [14, 19, 8, 8, 是], [14, 20, 10, 10, 是], [14, 21, 12, 12, 是], [14, 22, 14, 14, 是], [15, 0, 44, 44, 是], [15, 1, 0, 0, 是], [15, 2, 18, 18, 是], [15, 3, 20, 20, 是], [15, 4, 22, 22, 是], [15, 5, 24, 24, 是], [15, 6, 26, 26, 是], [15, 7, 28, 28, 是], [15, 8, 30, 30, 是], [15, 9, 32, 32, 是], [15, 10, 34, 34, 是], [15, 11, 36, 36, 是], [15, 12, 2, 2, 是], [15, 13, 38, 38, 是], [15, 14, 40, 40, 是], [15, 15, 42, 42, 是], [15, 16, 4, 4, 是], [15, 17, 6, 6, 是], [15, 18, 8, 8, 是], [15, 19, 10, 10, 是], [15, 20, 12, 12, 是], [15, 21, 14, 14, 是], [15, 22, 16, 16, 是], [16, 0, 6, 6, 是], [16, 1, 8, 8, 是], [16, 2, 26, 26, 是], [16, 3, 28, 28, 是], [16, 4, 30, 30, 是], [16, 5, 32, 32, 是], [16, 6, 34, 34, 是], [16, 7, 36, 36, 是], [16, 8, 38, 38, 是], [16, 9, 40, 40, 是], [16, 10, 42, 42, 是], [16, 11, 44, 44, 是], [16, 12, 10, 10, 是], [16, 13, 0, 0, 是], [16, 14, 2, 2, 是], [16, 15, 4, 4, 是], [16, 16, 12, 12, 是], [16, 17, 14, 14, 是], [16, 18, 16, 16, 是], [16, 19, 18, 18, 是], [16, 20, 20, 20, 是], [16, 21, 22, 22, 是], [16, 22, 24, 24, 是], [17, 0, 8, 8, 是], [17, 1, 10, 10, 是], [17, 2, 28, 28, 是], [17, 3, 30, 30, 是], [17, 4, 32, 32, 是], [17, 5, 34, 34, 是], [17, 6, 36, 36, 是], [17, 7, 38, 38, 是], [17, 8, 40, 40, 是], [17, 9, 42, 42, 是], [17, 10, 44, 44, 是], [17, 11, 0, 0, 是], [17, 12, 12, 12, 是], [17, 13, 2, 2, 是], [17, 14, 4, 4, 是], [17, 15, 6, 6, 是], [17, 16, 14, 14, 是], [17, 17, 16, 16, 是], [17, 18, 18, 18, 是], [17, 19, 20, 20, 是], [17, 20, 22, 22, 是], [17, 21, 24, 24, 是], [17, 22, 26, 26, 是], [18, 0, 10, 10, 是], [18, 1, 12, 12, 是], [18, 2, 30, 30, 是], [18, 3, 32, 32, 是], [18, 4, 34, 34, 是], [18, 5, 36, 36, 是], [18, 6, 38, 38, 是], [18, 7, 40, 40, 是], [18, 8, 42, 42, 是], [18, 9, 44, 44, 是], [18, 10, 0, 0, 是], [18, 11, 2, 2, 是], [18, 12, 14, 14, 是], [18, 13, 4, 4, 是], [18, 14, 6, 6, 是], [18, 15, 8, 8, 是], [18, 16, 16, 16, 是], [18, 17, 18, 18, 是], [18, 18, 20, 20, 是], [18, 19, 22, 22, 是], [18, 20, 24, 24, 是], [18, 21, 26, 26, 是], [18, 22, 28, 28, 是], [19, 0, 12, 12, 是], [19, 1, 14, 14, 是], [19, 2, 32, 32, 是], [19, 3, 34, 34, 是], [19, 4, 36, 36, 是], [19, 5, 38, 38, 是], [19, 6, 40, 40, 是], [19, 7, 42, 42, 是], [19, 8, 44, 44, 是], [19, 9, 0, 0, 是], [19, 10, 2, 2, 是], [19, 11, 4, 4, 是], [19, 12, 16, 16, 是], [19, 13, 6, 6, 是], [19, 14, 8, 8, 是], [19, 15, 10, 10, 是], [19, 16, 18, 18, 是], [19, 17, 20, 20, 是], [19, 18, 22, 22, 是], [19, 19, 24, 24, 是], [19, 20, 26, 26, 是], [19, 21, 28, 28, 是], [19, 22, 30, 30, 是], [20, 0, 14, 14, 是], [20, 1, 16, 16, 是], [20, 2, 34, 34, 是], [20, 3, 36, 36, 是], [20, 4, 38, 38, 是], [20, 5, 40, 40, 是], [20, 6, 42, 42, 是], [20, 7, 44, 44, 是], [20, 8, 0, 0, 是], [20, 9, 2, 2, 是], [20, 10, 4, 4, 是], [20, 11, 6, 6, 是], [20, 12, 18, 18, 是], [20, 13, 8, 8, 是], [20, 14, 10, 10, 是], [20, 15, 12, 12, 是], [20, 16, 20, 20, 是], [20, 17, 22, 22, 是], [20, 18, 24, 24, 是], [20, 19, 26, 26, 是], [20, 20, 28, 28, 是], [20, 21, 30, 30, 是], [20, 22, 32, 32, 是], [21, 0, 16, 16, 是], [21, 1, 18, 18, 是], [21, 2, 36, 36, 是], [21, 3, 38, 38, 是], [21, 4, 40, 40, 是], [21, 5, 42, 42, 是], [21, 6, 44, 44, 是], [21, 7, 0, 0, 是], [21, 8, 2, 2, 是], [21, 9, 4, 4, 是], [21, 10, 6, 6, 是], [21, 11, 8, 8, 是], [21, 12, 20, 20, 是], [21, 13, 10, 10, 是], [21, 14, 12, 12, 是], [21, 15, 14, 14, 是], [21, 16, 22, 22, 是], [21, 17, 24, 24, 是], [21, 18, 26, 26, 是], [21, 19, 28, 28, 是], [21, 20, 30, 30, 是], [21, 21, 32, 32, 是], [21, 22, 34, 34, 是], [22, 0, 18, 18, 是], [22, 1, 20, 20, 是], [22, 2, 38, 38, 是], [22, 3, 40, 40, 是], [22, 4, 42, 42, 是], [22, 5, 44, 44, 是], [22, 6, 0, 0, 是], [22, 7, 2, 2, 是], [22, 8, 4, 4, 是], [22, 9, 6, 6, 是], [22, 10, 8, 8, 是], [22, 11, 10, 10, 是], [22, 12, 22, 22, 是], [22, 13, 12, 12, 是], [22, 14, 14, 14, 是], [22, 15, 16, 16, 是], [22, 16, 24, 24, 是], [22, 17, 26, 26, 是], [22, 18, 28, 28, 是], [22, 19, 30, 30, 是], [22, 20, 32, 32, 是], [22, 21, 34, 34, 是], [22, 22, 36, 36, 是]], 是, 是, 是, 是, 否] 條件：無 bar_f保乘法由f(ab)=f(a)f(b)；若f(a)=f(b)，a^-1b∈K故同coset，給injective。任意image值f(g)由gK命中，給onto IMAGE；不由同cardinality代替這些責任，也不自動onto整個target。 步驟識別與依賴規則：Iso1_ALL_induced_product_pairs_injective_and_onto_IMAGE_separate · 依賴：G001, S009 S011 · implies操作前 source roles = [[0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44], 46, 23] 操作後 derived = [否, G/kernel_is_isomorphic_to_image, non_surjective_f_does_not_identify_the_quotient_with_the_whole_codomain, 否] 條件：無 只有實際f滿射，image才等同整個codomain。最後No保一般抽象證明／形式化責任，不否定本題完整有限同構證書或教學理由。 步驟識別與依賴規則：Iso1_image_VS_codomain_scope_and_finite_general_proof_boundary · 依賴：G001, S010 ## 逐步反向核對 - S011 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。 - S010 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。 - S009 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。 - S008 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。 - S007 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。 - S006 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。 - S005 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。 - S004 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。 - S003 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。 - S002 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。 - S001 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。 ## 結論 ([0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44], 46, 23, 否, G/kernel_is_isomorphic_to_image, non_surjective_f_does_not_identify_the_quotient_with_the_whole_codomain, 否, finite_instance_certificate_not_a_general_theorem_proof) 依上列完整代值及條件核對得到原題答案；原題編號、格式與狀態保持不變。 ## 本題覆核與來源綁定 覆核日期：2026-10-26 原題、答案、步驟表達式、數值 AST 與既有歷史保持原樣；原來的候選狀態屬於來源歷史，不覆寫為形式化證明。 來源雜湊與覆核憑證 - input commit: 0f7be61e2c22317a4075561dc822c87d881a50db - original question SHA-256: f6592782b4ec2fb570116c3c75571721a804f759c83983e9bbc4c47e226d0a47 - candidate record SHA-256: 68877d3e295c436d2d21575064828d60fe45de565560ca3929274359757c6456 - semantic review receipt SHA-256: 74c63a2c12285a3b2073f8d9f102bc2ba5fb7ed890c5b7c3b8afa94f032eda82 - question-first witness SHA-256: 6d56428610f8e86c45fd00a2ad3b27ad9c052956946f0b91d71a68536f79d95f - Lean: NOT_RUN · human review: NOT_PERFORMED [同源完整 JSON](https://ocme.evemisslab.com/data/question-derivations/questions/q-20261015-advance-20261115-r01-first-isomorphism-theorem-finite-groups-0097.json)