# 第 25695 題：有限群中心 [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-r02-finite-group-center-foundations/#q-20261015-advance-20261115-r02-finite-group-center-0045) 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。 R0050-25695 · q-20261015-advance-20261115-r02-finite-group-center-0045 ## 原題與已知條件 完整Cayley table上的forall-g commutation與center資格。操作=center-subgroup-audit；資料={"group_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],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,0,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,22],[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,0,1,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,22,23],[3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,0,1,2,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,22,23,24],[4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,0,1,2,3,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,22,23,24,25],[5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,0,1,2,3,4,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,22,23,24,25,26],[6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,0,1,2,3,4,5,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,22,23,24,25,26,27],[7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,0,1,2,3,4,5,6,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,22,23,24,25,26,27,28],[8,9,10,11,12,13,14,15,16,17,18,19,20,21,0,1,2,3,4,5,6,7,30,31,32,33,34,35,36,37,38,39,40,41,42,43,22,23,24,25,26,27,28,29],[9,10,11,12,13,14,15,16,17,18,19,20,21,0,1,2,3,4,5,6,7,8,31,32,33,34,35,36,37,38,39,40,41,42,43,22,23,24,25,26,27,28,29,30],[10,11,12,13,14,15,16,17,18,19,20,21,0,1,2,3,4,5,6,7,8,9,32,33,34,35,36,37,38,39,40,41,42,43,22,23,24,25,26,27,28,29,30,31],[11,12,13,14,15,16,17,18,19,20,21,0,1,2,3,4,5,6,7,8,9,10,33,34,35,36,37,38,39,40,41,42,43,22,23,24,25,26,27,28,29,30,31,32],[12,13,14,15,16,17,18,19,20,21,0,1,2,3,4,5,6,7,8,9,10,11,34,35,36,37,38,39,40,41,42,43,22,23,24,25,26,27,28,29,30,31,32,33],[13,14,15,16,17,18,19,20,21,0,1,2,3,4,5,6,7,8,9,10,11,12,35,36,37,38,39,40,41,42,43,22,23,24,25,26,27,28,29,30,31,32,33,34],[14,15,16,17,18,19,20,21,0,1,2,3,4,5,6,7,8,9,10,11,12,13,36,37,38,39,40,41,42,43,22,23,24,25,26,27,28,29,30,31,32,33,34,35],[15,16,17,18,19,20,21,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,37,38,39,40,41,42,43,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36],[16,17,18,19,20,21,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,38,39,40,41,42,43,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37],[17,18,19,20,21,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,39,40,41,42,43,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38],[18,19,20,21,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,40,41,42,43,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39],[19,20,21,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,41,42,43,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40],[20,21,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,42,43,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41],[21,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,43,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42],[22,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,0,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1],[23,22,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,1,0,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2],[24,23,22,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,2,1,0,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3],[25,24,23,22,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,3,2,1,0,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4],[26,25,24,23,22,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,4,3,2,1,0,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5],[27,26,25,24,23,22,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,5,4,3,2,1,0,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6],[28,27,26,25,24,23,22,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,6,5,4,3,2,1,0,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7],[29,28,27,26,25,24,23,22,43,42,41,40,39,38,37,36,35,34,33,32,31,30,7,6,5,4,3,2,1,0,21,20,19,18,17,16,15,14,13,12,11,10,9,8],[30,29,28,27,26,25,24,23,22,43,42,41,40,39,38,37,36,35,34,33,32,31,8,7,6,5,4,3,2,1,0,21,20,19,18,17,16,15,14,13,12,11,10,9],[31,30,29,28,27,26,25,24,23,22,43,42,41,40,39,38,37,36,35,34,33,32,9,8,7,6,5,4,3,2,1,0,21,20,19,18,17,16,15,14,13,12,11,10],[32,31,30,29,28,27,26,25,24,23,22,43,42,41,40,39,38,37,36,35,34,33,10,9,8,7,6,5,4,3,2,1,0,21,20,19,18,17,16,15,14,13,12,11],[33,32,31,30,29,28,27,26,25,24,23,22,43,42,41,40,39,38,37,36,35,34,11,10,9,8,7,6,5,4,3,2,1,0,21,20,19,18,17,16,15,14,13,12],[34,33,32,31,30,29,28,27,26,25,24,23,22,43,42,41,40,39,38,37,36,35,12,11,10,9,8,7,6,5,4,3,2,1,0,21,20,19,18,17,16,15,14,13],[35,34,33,32,31,30,29,28,27,26,25,24,23,22,43,42,41,40,39,38,37,36,13,12,11,10,9,8,7,6,5,4,3,2,1,0,21,20,19,18,17,16,15,14],[36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,43,42,41,40,39,38,37,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,21,20,19,18,17,16,15],[37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,43,42,41,40,39,38,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,21,20,19,18,17,16],[38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,43,42,41,40,39,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,21,20,19,18,17],[39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,43,42,41,40,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,21,20,19,18],[40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,43,42,41,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,21,20,19],[41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,43,42,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,21,20],[42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,43,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,21],[43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0]],"identity":0}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。 - G001 — 完整Cayley table上的forall-g commutation與center資格。操作=center-subgroup-audit；資料={"group_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],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,0,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,22],[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,0,1,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,22,23],[3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,0,1,2,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,22,23,24],[4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,0,1,2,3,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,22,23,24,25],[5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,0,1,2,3,4,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,22,23,24,25,26],[6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,0,1,2,3,4,5,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,22,23,24,25,26,27],[7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,0,1,2,3,4,5,6,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,22,23,24,25,26,27,28],[8,9,10,11,12,13,14,15,16,17,18,19,20,21,0,1,2,3,4,5,6,7,30,31,32,33,34,35,36,37,38,39,40,41,42,43,22,23,24,25,26,27,28,29],[9,10,11,12,13,14,15,16,17,18,19,20,21,0,1,2,3,4,5,6,7,8,31,32,33,34,35,36,37,38,39,40,41,42,43,22,23,24,25,26,27,28,29,30],[10,11,12,13,14,15,16,17,18,19,20,21,0,1,2,3,4,5,6,7,8,9,32,33,34,35,36,37,38,39,40,41,42,43,22,23,24,25,26,27,28,29,30,31],[11,12,13,14,15,16,17,18,19,20,21,0,1,2,3,4,5,6,7,8,9,10,33,34,35,36,37,38,39,40,41,42,43,22,23,24,25,26,27,28,29,30,31,32],[12,13,14,15,16,17,18,19,20,21,0,1,2,3,4,5,6,7,8,9,10,11,34,35,36,37,38,39,40,41,42,43,22,23,24,25,26,27,28,29,30,31,32,33],[13,14,15,16,17,18,19,20,21,0,1,2,3,4,5,6,7,8,9,10,11,12,35,36,37,38,39,40,41,42,43,22,23,24,25,26,27,28,29,30,31,32,33,34],[14,15,16,17,18,19,20,21,0,1,2,3,4,5,6,7,8,9,10,11,12,13,36,37,38,39,40,41,42,43,22,23,24,25,26,27,28,29,30,31,32,33,34,35],[15,16,17,18,19,20,21,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,37,38,39,40,41,42,43,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36],[16,17,18,19,20,21,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,38,39,40,41,42,43,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37],[17,18,19,20,21,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,39,40,41,42,43,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38],[18,19,20,21,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,40,41,42,43,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39],[19,20,21,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,41,42,43,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40],[20,21,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,42,43,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41],[21,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,43,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42],[22,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,0,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1],[23,22,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,1,0,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2],[24,23,22,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,2,1,0,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3],[25,24,23,22,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,3,2,1,0,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4],[26,25,24,23,22,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,4,3,2,1,0,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5],[27,26,25,24,23,22,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,5,4,3,2,1,0,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6],[28,27,26,25,24,23,22,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,6,5,4,3,2,1,0,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7],[29,28,27,26,25,24,23,22,43,42,41,40,39,38,37,36,35,34,33,32,31,30,7,6,5,4,3,2,1,0,21,20,19,18,17,16,15,14,13,12,11,10,9,8],[30,29,28,27,26,25,24,23,22,43,42,41,40,39,38,37,36,35,34,33,32,31,8,7,6,5,4,3,2,1,0,21,20,19,18,17,16,15,14,13,12,11,10,9],[31,30,29,28,27,26,25,24,23,22,43,42,41,40,39,38,37,36,35,34,33,32,9,8,7,6,5,4,3,2,1,0,21,20,19,18,17,16,15,14,13,12,11,10],[32,31,30,29,28,27,26,25,24,23,22,43,42,41,40,39,38,37,36,35,34,33,10,9,8,7,6,5,4,3,2,1,0,21,20,19,18,17,16,15,14,13,12,11],[33,32,31,30,29,28,27,26,25,24,23,22,43,42,41,40,39,38,37,36,35,34,11,10,9,8,7,6,5,4,3,2,1,0,21,20,19,18,17,16,15,14,13,12],[34,33,32,31,30,29,28,27,26,25,24,23,22,43,42,41,40,39,38,37,36,35,12,11,10,9,8,7,6,5,4,3,2,1,0,21,20,19,18,17,16,15,14,13],[35,34,33,32,31,30,29,28,27,26,25,24,23,22,43,42,41,40,39,38,37,36,13,12,11,10,9,8,7,6,5,4,3,2,1,0,21,20,19,18,17,16,15,14],[36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,43,42,41,40,39,38,37,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,21,20,19,18,17,16,15],[37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,43,42,41,40,39,38,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,21,20,19,18,17,16],[38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,43,42,41,40,39,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,21,20,19,18,17],[39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,43,42,41,40,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,21,20,19,18],[40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,43,42,41,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,21,20,19],[41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,43,42,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,21,20],[42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,43,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,21],[43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0]],"identity":0}。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-finite-group-center](https://ocme.evemisslab.com/zh-Hant/mko/mko-finite-group-center/) ## 逐步推導 S001 · implies操作前 source roles = [center-subgroup-audit] 操作後 derived = [[center, contains_identity, product_closed, inverse_closed, subgroup, certificate]] 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 = [Center ORIGINAL group, [[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], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 0, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 22], [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 0, 1, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 22, 23], [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 0, 1, 2, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 22, 23, 24], [4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 0, 1, 2, 3, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 22, 23, 24, 25], [5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 0, 1, 2, 3, 4, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 22, 23, 24, 25, 26], [6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 0, 1, 2, 3, 4, 5, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 22, 23, 24, 25, 26, 27], [7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 0, 1, 2, 3, 4, 5, 6, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 22, 23, 24, 25, 26, 27, 28], [8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 0, 1, 2, 3, 4, 5, 6, 7, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 22, 23, 24, 25, 26, 27, 28, 29], [9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 0, 1, 2, 3, 4, 5, 6, 7, 8, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 22, 23, 24, 25, 26, 27, 28, 29, 30], [10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31], [11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32], [12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33], [13, 14, 15, 16, 17, 18, 19, 20, 21, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 35, 36, 37, 38, 39, 40, 41, 42, 43, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34], [14, 15, 16, 17, 18, 19, 20, 21, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 36, 37, 38, 39, 40, 41, 42, 43, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35], [15, 16, 17, 18, 19, 20, 21, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 37, 38, 39, 40, 41, 42, 43, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36], [16, 17, 18, 19, 20, 21, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 38, 39, 40, 41, 42, 43, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37], [17, 18, 19, 20, 21, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 39, 40, 41, 42, 43, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38], [18, 19, 20, 21, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 40, 41, 42, 43, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39], [19, 20, 21, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 41, 42, 43, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40], [20, 21, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 42, 43, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41], [21, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 43, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42], [22, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 0, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1], [23, 22, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 1, 0, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2], [24, 23, 22, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 2, 1, 0, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3], [25, 24, 23, 22, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 3, 2, 1, 0, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4], [26, 25, 24, 23, 22, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 4, 3, 2, 1, 0, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5], [27, 26, 25, 24, 23, 22, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 5, 4, 3, 2, 1, 0, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6], [28, 27, 26, 25, 24, 23, 22, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 6, 5, 4, 3, 2, 1, 0, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7], [29, 28, 27, 26, 25, 24, 23, 22, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 7, 6, 5, 4, 3, 2, 1, 0, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8], [30, 29, 28, 27, 26, 25, 24, 23, 22, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 8, 7, 6, 5, 4, 3, 2, 1, 0, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9], [31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10], [32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11], [33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12], [34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 43, 42, 41, 40, 39, 38, 37, 36, 35, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 21, 20, 19, 18, 17, 16, 15, 14, 13], [35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 43, 42, 41, 40, 39, 38, 37, 36, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 21, 20, 19, 18, 17, 16, 15, 14], [36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 43, 42, 41, 40, 39, 38, 37, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 21, 20, 19, 18, 17, 16, 15], [37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 43, 42, 41, 40, 39, 38, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 21, 20, 19, 18, 17, 16], [38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 43, 42, 41, 40, 39, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 21, 20, 19, 18, 17], [39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 43, 42, 41, 40, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 21, 20, 19, 18], [40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 43, 42, 41, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 21, 20, 19], [41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 43, 42, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 21, 20], [42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 43, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 21], [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, 0]], 0] 操作後 derived = [44, [[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]], 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 = [Center ORIGINAL group, 44, 0] 操作後 derived = [[[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, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是]], 85184, [0, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43]] 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 = [0, [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]] 操作後 derived = [[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], [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], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], 是] 條件：無 逐z比較zg與gz的完整row，不以某一g的centralizer代替Z(G)。 步驟識別與依賴規則：Center_EVERY_z_commutes_against_EVERY_g · 依賴：G001, S003 S005 · implies操作前 source roles = [1, [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]] 操作後 derived = [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 0, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 22], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 0, 43, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否], 否] 條件：無 逐z比較zg與gz的完整row，不以某一g的centralizer代替Z(G)。 步驟識別與依賴規則：Center_EVERY_z_commutes_against_EVERY_g · 依賴：G001, S004 S006 · implies操作前 source roles = [2, [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]] 操作後 derived = [[2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 0, 1, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 22, 23], [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 0, 1, 42, 43, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否], 否] 條件：無 逐z比較zg與gz的完整row，不以某一g的centralizer代替Z(G)。 步驟識別與依賴規則：Center_EVERY_z_commutes_against_EVERY_g · 依賴：G001, S005 S007 · implies操作前 source roles = [3, [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]] 操作後 derived = [[3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 0, 1, 2, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 22, 23, 24], [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 0, 1, 2, 41, 42, 43, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否], 否] 條件：無 逐z比較zg與gz的完整row，不以某一g的centralizer代替Z(G)。 步驟識別與依賴規則：Center_EVERY_z_commutes_against_EVERY_g · 依賴：G001, S006 S008 · implies操作前 source roles = [4, [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]] 操作後 derived = [[4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 0, 1, 2, 3, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 22, 23, 24, 25], [4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 0, 1, 2, 3, 40, 41, 42, 43, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否], 否] 條件：無 逐z比較zg與gz的完整row，不以某一g的centralizer代替Z(G)。 步驟識別與依賴規則：Center_EVERY_z_commutes_against_EVERY_g · 依賴：G001, S007 S009 · implies操作前 source roles = [5, [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]] 操作後 derived = [[5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 0, 1, 2, 3, 4, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 22, 23, 24, 25, 26], [5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 0, 1, 2, 3, 4, 39, 40, 41, 42, 43, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否], 否] 條件：無 逐z比較zg與gz的完整row，不以某一g的centralizer代替Z(G)。 步驟識別與依賴規則：Center_EVERY_z_commutes_against_EVERY_g · 依賴：G001, S008 S010 · implies操作前 source roles = [6, [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]] 操作後 derived = [[6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 0, 1, 2, 3, 4, 5, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 22, 23, 24, 25, 26, 27], [6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 0, 1, 2, 3, 4, 5, 38, 39, 40, 41, 42, 43, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否], 否] 條件：無 逐z比較zg與gz的完整row，不以某一g的centralizer代替Z(G)。 步驟識別與依賴規則：Center_EVERY_z_commutes_against_EVERY_g · 依賴：G001, S009 S011 · implies操作前 source roles = [7, [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]] 操作後 derived = [[7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 0, 1, 2, 3, 4, 5, 6, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 22, 23, 24, 25, 26, 27, 28], [7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 0, 1, 2, 3, 4, 5, 6, 37, 38, 39, 40, 41, 42, 43, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否], 否] 條件：無 逐z比較zg與gz的完整row，不以某一g的centralizer代替Z(G)。 步驟識別與依賴規則：Center_EVERY_z_commutes_against_EVERY_g · 依賴：G001, S010 S012 · implies操作前 source roles = [8, [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]] 操作後 derived = [[8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 0, 1, 2, 3, 4, 5, 6, 7, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 22, 23, 24, 25, 26, 27, 28, 29], [8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 0, 1, 2, 3, 4, 5, 6, 7, 36, 37, 38, 39, 40, 41, 42, 43, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否], 否] 條件：無 逐z比較zg與gz的完整row，不以某一g的centralizer代替Z(G)。 步驟識別與依賴規則：Center_EVERY_z_commutes_against_EVERY_g · 依賴：G001, S011 S013 · implies操作前 source roles = [9, [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]] 操作後 derived = [[9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 0, 1, 2, 3, 4, 5, 6, 7, 8, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 22, 23, 24, 25, 26, 27, 28, 29, 30], [9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 0, 1, 2, 3, 4, 5, 6, 7, 8, 35, 36, 37, 38, 39, 40, 41, 42, 43, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否], 否] 條件：無 逐z比較zg與gz的完整row，不以某一g的centralizer代替Z(G)。 步驟識別與依賴規則：Center_EVERY_z_commutes_against_EVERY_g · 依賴：G001, S012 S014 · implies操作前 source roles = [10, [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]] 操作後 derived = [[10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31], [10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否], 否] 條件：無 逐z比較zg與gz的完整row，不以某一g的centralizer代替Z(G)。 步驟識別與依賴規則：Center_EVERY_z_commutes_against_EVERY_g · 依賴：G001, S013 S015 · implies操作前 source roles = [11, [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]] 操作後 derived = [[11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32], [11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], 是] 條件：無 逐z比較zg與gz的完整row，不以某一g的centralizer代替Z(G)。 步驟識別與依賴規則：Center_EVERY_z_commutes_against_EVERY_g · 依賴：G001, S014 S016 · implies操作前 source roles = [12, [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]] 操作後 derived = [[12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33], [12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否], 否] 條件：無 逐z比較zg與gz的完整row，不以某一g的centralizer代替Z(G)。 步驟識別與依賴規則：Center_EVERY_z_commutes_against_EVERY_g · 依賴：G001, S015 S017 · implies操作前 source roles = [13, [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]] 操作後 derived = [[13, 14, 15, 16, 17, 18, 19, 20, 21, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 35, 36, 37, 38, 39, 40, 41, 42, 43, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34], [13, 14, 15, 16, 17, 18, 19, 20, 21, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 22, 23, 24, 25, 26, 27, 28, 29, 30], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否], 否] 條件：無 逐z比較zg與gz的完整row，不以某一g的centralizer代替Z(G)。 步驟識別與依賴規則：Center_EVERY_z_commutes_against_EVERY_g · 依賴：G001, S016 S018 · implies操作前 source roles = [14, [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]] 操作後 derived = [[14, 15, 16, 17, 18, 19, 20, 21, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 36, 37, 38, 39, 40, 41, 42, 43, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35], [14, 15, 16, 17, 18, 19, 20, 21, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 22, 23, 24, 25, 26, 27, 28, 29], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否], 否] 條件：無 逐z比較zg與gz的完整row，不以某一g的centralizer代替Z(G)。 步驟識別與依賴規則：Center_EVERY_z_commutes_against_EVERY_g · 依賴：G001, S017 S019 · implies操作前 source roles = [15, [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]] 操作後 derived = [[15, 16, 17, 18, 19, 20, 21, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 37, 38, 39, 40, 41, 42, 43, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36], [15, 16, 17, 18, 19, 20, 21, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 22, 23, 24, 25, 26, 27, 28], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否], 否] 條件：無 逐z比較zg與gz的完整row，不以某一g的centralizer代替Z(G)。 步驟識別與依賴規則：Center_EVERY_z_commutes_against_EVERY_g · 依賴：G001, S018 S020 · implies操作前 source roles = [16, [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]] 操作後 derived = [[16, 17, 18, 19, 20, 21, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 38, 39, 40, 41, 42, 43, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37], [16, 17, 18, 19, 20, 21, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 22, 23, 24, 25, 26, 27], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否], 否] 條件：無 逐z比較zg與gz的完整row，不以某一g的centralizer代替Z(G)。 步驟識別與依賴規則：Center_EVERY_z_commutes_against_EVERY_g · 依賴：G001, S019 S021 · implies操作前 source roles = [17, [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]] 操作後 derived = [[17, 18, 19, 20, 21, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 39, 40, 41, 42, 43, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38], [17, 18, 19, 20, 21, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 22, 23, 24, 25, 26], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否], 否] 條件：無 逐z比較zg與gz的完整row，不以某一g的centralizer代替Z(G)。 步驟識別與依賴規則：Center_EVERY_z_commutes_against_EVERY_g · 依賴：G001, S020 S022 · implies操作前 source roles = [18, [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]] 操作後 derived = [[18, 19, 20, 21, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 40, 41, 42, 43, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39], [18, 19, 20, 21, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 22, 23, 24, 25], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否], 否] 條件：無 逐z比較zg與gz的完整row，不以某一g的centralizer代替Z(G)。 步驟識別與依賴規則：Center_EVERY_z_commutes_against_EVERY_g · 依賴：G001, S021 S023 · implies操作前 source roles = [19, [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]] 操作後 derived = [[19, 20, 21, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 41, 42, 43, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40], [19, 20, 21, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 22, 23, 24], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否], 否] 條件：無 逐z比較zg與gz的完整row，不以某一g的centralizer代替Z(G)。 步驟識別與依賴規則：Center_EVERY_z_commutes_against_EVERY_g · 依賴：G001, S022 S024 · implies操作前 source roles = [20, [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]] 操作後 derived = [[20, 21, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 42, 43, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41], [20, 21, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 22, 23], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否], 否] 條件：無 逐z比較zg與gz的完整row，不以某一g的centralizer代替Z(G)。 步驟識別與依賴規則：Center_EVERY_z_commutes_against_EVERY_g · 依賴：G001, S023 S025 · implies操作前 source roles = [21, [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]] 操作後 derived = [[21, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 43, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42], [21, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 22], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否], 否] 條件：無 逐z比較zg與gz的完整row，不以某一g的centralizer代替Z(G)。 步驟識別與依賴規則：Center_EVERY_z_commutes_against_EVERY_g · 依賴：G001, S024 S026 · implies操作前 source roles = [22, [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]] 操作後 derived = [[22, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 0, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1], [22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21], [是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否], 否] 條件：無 逐z比較zg與gz的完整row，不以某一g的centralizer代替Z(G)。 步驟識別與依賴規則：Center_EVERY_z_commutes_against_EVERY_g · 依賴：G001, S025 S027 · implies操作前 source roles = [23, [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]] 操作後 derived = [[23, 22, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 1, 0, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2], [23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 22, 21, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20], [是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否], 否] 條件：無 逐z比較zg與gz的完整row，不以某一g的centralizer代替Z(G)。 步驟識別與依賴規則：Center_EVERY_z_commutes_against_EVERY_g · 依賴：G001, S026 S028 · implies操作前 source roles = [24, [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]] 操作後 derived = [[24, 23, 22, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 2, 1, 0, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3], [24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 22, 23, 20, 21, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19], [是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否], 否] 條件：無 逐z比較zg與gz的完整row，不以某一g的centralizer代替Z(G)。 步驟識別與依賴規則：Center_EVERY_z_commutes_against_EVERY_g · 依賴：G001, S027 S029 · implies操作前 source roles = [25, [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]] 操作後 derived = [[25, 24, 23, 22, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 3, 2, 1, 0, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4], [25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 22, 23, 24, 19, 20, 21, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18], [是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否], 否] 條件：無 逐z比較zg與gz的完整row，不以某一g的centralizer代替Z(G)。 步驟識別與依賴規則：Center_EVERY_z_commutes_against_EVERY_g · 依賴：G001, S028 S030 · implies操作前 source roles = [26, [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]] 操作後 derived = [[26, 25, 24, 23, 22, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 4, 3, 2, 1, 0, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5], [26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 22, 23, 24, 25, 18, 19, 20, 21, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17], [是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否], 否] 條件：無 逐z比較zg與gz的完整row，不以某一g的centralizer代替Z(G)。 步驟識別與依賴規則：Center_EVERY_z_commutes_against_EVERY_g · 依賴：G001, S029 S031 · implies操作前 source roles = [27, [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]] 操作後 derived = [[27, 26, 25, 24, 23, 22, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 5, 4, 3, 2, 1, 0, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6], [27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 22, 23, 24, 25, 26, 17, 18, 19, 20, 21, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16], [是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否], 否] 條件：無 逐z比較zg與gz的完整row，不以某一g的centralizer代替Z(G)。 步驟識別與依賴規則：Center_EVERY_z_commutes_against_EVERY_g · 依賴：G001, S030 S032 · implies操作前 source roles = [28, [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]] 操作後 derived = [[28, 27, 26, 25, 24, 23, 22, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 6, 5, 4, 3, 2, 1, 0, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7], [28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 22, 23, 24, 25, 26, 27, 16, 17, 18, 19, 20, 21, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15], [是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否], 否] 條件：無 逐z比較zg與gz的完整row，不以某一g的centralizer代替Z(G)。 步驟識別與依賴規則：Center_EVERY_z_commutes_against_EVERY_g · 依賴：G001, S031 S033 · implies操作前 source roles = [29, [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]] 操作後 derived = [[29, 28, 27, 26, 25, 24, 23, 22, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 7, 6, 5, 4, 3, 2, 1, 0, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8], [29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 22, 23, 24, 25, 26, 27, 28, 15, 16, 17, 18, 19, 20, 21, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14], [是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否], 否] 條件：無 逐z比較zg與gz的完整row，不以某一g的centralizer代替Z(G)。 步驟識別與依賴規則：Center_EVERY_z_commutes_against_EVERY_g · 依賴：G001, S032 S034 · implies操作前 source roles = [30, [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]] 操作後 derived = [[30, 29, 28, 27, 26, 25, 24, 23, 22, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 8, 7, 6, 5, 4, 3, 2, 1, 0, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9], [30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 22, 23, 24, 25, 26, 27, 28, 29, 14, 15, 16, 17, 18, 19, 20, 21, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13], [是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否], 否] 條件：無 逐z比較zg與gz的完整row，不以某一g的centralizer代替Z(G)。 步驟識別與依賴規則：Center_EVERY_z_commutes_against_EVERY_g · 依賴：G001, S033 S035 · implies操作前 source roles = [31, [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]] 操作後 derived = [[31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10], [31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 22, 23, 24, 25, 26, 27, 28, 29, 30, 13, 14, 15, 16, 17, 18, 19, 20, 21, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], [是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否], 否] 條件：無 逐z比較zg與gz的完整row，不以某一g的centralizer代替Z(G)。 步驟識別與依賴規則：Center_EVERY_z_commutes_against_EVERY_g · 依賴：G001, S034 S036 · implies操作前 source roles = [32, [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]] 操作後 derived = [[32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11], [32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是], 否] 條件：無 逐z比較zg與gz的完整row，不以某一g的centralizer代替Z(G)。 步驟識別與依賴規則：Center_EVERY_z_commutes_against_EVERY_g · 依賴：G001, S035 S037 · implies操作前 source roles = [33, [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]] 操作後 derived = [[33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12], [33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10], [是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否], 否] 條件：無 逐z比較zg與gz的完整row，不以某一g的centralizer代替Z(G)。 步驟識別與依賴規則：Center_EVERY_z_commutes_against_EVERY_g · 依賴：G001, S036 S038 · implies操作前 source roles = [34, [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]] 操作後 derived = [[34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 43, 42, 41, 40, 39, 38, 37, 36, 35, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 21, 20, 19, 18, 17, 16, 15, 14, 13], [34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否], 否] 條件：無 逐z比較zg與gz的完整row，不以某一g的centralizer代替Z(G)。 步驟識別與依賴規則：Center_EVERY_z_commutes_against_EVERY_g · 依賴：G001, S037 S039 · implies操作前 source roles = [35, [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]] 操作後 derived = [[35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 43, 42, 41, 40, 39, 38, 37, 36, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 21, 20, 19, 18, 17, 16, 15, 14], [35, 36, 37, 38, 39, 40, 41, 42, 43, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 0, 1, 2, 3, 4, 5, 6, 7, 8], [是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否], 否] 條件：無 逐z比較zg與gz的完整row，不以某一g的centralizer代替Z(G)。 步驟識別與依賴規則：Center_EVERY_z_commutes_against_EVERY_g · 依賴：G001, S038 S040 · implies操作前 source roles = [36, [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]] 操作後 derived = [[36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 43, 42, 41, 40, 39, 38, 37, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 21, 20, 19, 18, 17, 16, 15], [36, 37, 38, 39, 40, 41, 42, 43, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 0, 1, 2, 3, 4, 5, 6, 7], [是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否], 否] 條件：無 逐z比較zg與gz的完整row，不以某一g的centralizer代替Z(G)。 步驟識別與依賴規則：Center_EVERY_z_commutes_against_EVERY_g · 依賴：G001, S039 S041 · implies操作前 source roles = [37, [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]] 操作後 derived = [[37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 43, 42, 41, 40, 39, 38, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 21, 20, 19, 18, 17, 16], [37, 38, 39, 40, 41, 42, 43, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 0, 1, 2, 3, 4, 5, 6], [是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否], 否] 條件：無 逐z比較zg與gz的完整row，不以某一g的centralizer代替Z(G)。 步驟識別與依賴規則：Center_EVERY_z_commutes_against_EVERY_g · 依賴：G001, S040 S042 · implies操作前 source roles = [38, [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]] 操作後 derived = [[38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 43, 42, 41, 40, 39, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 21, 20, 19, 18, 17], [38, 39, 40, 41, 42, 43, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 0, 1, 2, 3, 4, 5], [是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否], 否] 條件：無 逐z比較zg與gz的完整row，不以某一g的centralizer代替Z(G)。 步驟識別與依賴規則：Center_EVERY_z_commutes_against_EVERY_g · 依賴：G001, S041 S043 · implies操作前 source roles = [39, [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]] 操作後 derived = [[39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 43, 42, 41, 40, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 21, 20, 19, 18], [39, 40, 41, 42, 43, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 0, 1, 2, 3, 4], [是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否], 否] 條件：無 逐z比較zg與gz的完整row，不以某一g的centralizer代替Z(G)。 步驟識別與依賴規則：Center_EVERY_z_commutes_against_EVERY_g · 依賴：G001, S042 S044 · implies操作前 source roles = [40, [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]] 操作後 derived = [[40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 43, 42, 41, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 21, 20, 19], [40, 41, 42, 43, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 0, 1, 2, 3], [是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否], 否] 條件：無 逐z比較zg與gz的完整row，不以某一g的centralizer代替Z(G)。 步驟識別與依賴規則：Center_EVERY_z_commutes_against_EVERY_g · 依賴：G001, S043 S045 · implies操作前 source roles = [41, [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]] 操作後 derived = [[41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 43, 42, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 21, 20], [41, 42, 43, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 0, 1, 2], [是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否], 否] 條件：無 逐z比較zg與gz的完整row，不以某一g的centralizer代替Z(G)。 步驟識別與依賴規則：Center_EVERY_z_commutes_against_EVERY_g · 依賴：G001, S044 S046 · implies操作前 source roles = [42, [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]] 操作後 derived = [[42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 43, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 21], [42, 43, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 0, 1], [是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否], 否] 條件：無 逐z比較zg與gz的完整row，不以某一g的centralizer代替Z(G)。 步驟識別與依賴規則：Center_EVERY_z_commutes_against_EVERY_g · 依賴：G001, S045 S047 · implies操作前 source roles = [43, [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]] 操作後 derived = [[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, 0], [43, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 0], [是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是], 否] 條件：無 逐z比較zg與gz的完整row，不以某一g的centralizer代替Z(G)。 步驟識別與依賴規則：Center_EVERY_z_commutes_against_EVERY_g · 依賴：G001, S046 S048 · implies操作前 source roles = [Center ACTUAL Z, [0, 11], 0] 操作後 derived = [是, [[0, 0, 0, 是], [0, 11, 11, 是], [11, 0, 11, 是], [11, 11, 0, 是]], 是, [[0, 0, 是], [11, 11, 是]], 是, 是, [[0, [0, 11], 是], [1, [0, 11], 是], [2, [0, 11], 是], [3, [0, 11], 是], [4, [0, 11], 是], [5, [0, 11], 是], [6, [0, 11], 是], [7, [0, 11], 是], [8, [0, 11], 是], [9, [0, 11], 是], [10, [0, 11], 是], [11, [0, 11], 是], [12, [0, 11], 是], [13, [0, 11], 是], [14, [0, 11], 是], [15, [0, 11], 是], [16, [0, 11], 是], [17, [0, 11], 是], [18, [0, 11], 是], [19, [0, 11], 是], [20, [0, 11], 是], [21, [0, 11], 是], [22, [0, 11], 是], [23, [0, 11], 是], [24, [0, 11], 是], [25, [0, 11], 是], [26, [0, 11], 是], [27, [0, 11], 是], [28, [0, 11], 是], [29, [0, 11], 是], [30, [0, 11], 是], [31, [0, 11], 是], [32, [0, 11], 是], [33, [0, 11], 是], [34, [0, 11], 是], [35, [0, 11], 是], [36, [0, 11], 是], [37, [0, 11], 是], [38, [0, 11], 是], [39, [0, 11], 是], [40, [0, 11], 是], [41, [0, 11], 是], [42, [0, 11], 是], [43, [0, 11], 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, S047 S049 · implies操作前 source roles = [[0, 11], [[是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否], [是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否], [是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否], [是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否], [是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否], [是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否], [是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否], [是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否], [是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否], [是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否], [是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否], [是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是], [是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否], [是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否], [是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否], [是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否], [是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否], [是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否], [是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否], [是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否], [是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否], [是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否], [是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是]]] 操作後 derived = [是, 是, central z: g*z*g^-1=z for EVERY g] 條件：無 identity與每個g交換；z,w都與所有g交換則zw亦然，z^-1亦然。gz=zg右乘g^-1得gzg^-1=z，故每個central元素逐點固定而normal。不宣稱characteristic或class equation。 步驟識別與依賴規則：Center_GENERAL_closure_and_pointwise_fixed_conjugation · 依賴：G001, S048 ## 逐步反向核對 - S049 · 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。 - S048 · 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。 - S047 · 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。 - S046 · 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。 - S045 · 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。 - S044 · 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。 - S043 · 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。 - S042 · 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。 - S041 · 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。 - S040 · 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。 - S039 · 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。 - S038 · 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。 - S037 · 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。 - S036 · 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。 - S035 · 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。 - S034 · 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。 - S033 · 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。 - S032 · 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。 - S031 · 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。 - S030 · 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。 - S029 · 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。 - S028 · 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。 - S027 · 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。 - S026 · 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。 - S025 · 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。 - S024 · 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。 - S023 · 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。 - S022 · 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。 - S021 · 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。 - S020 · 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。 - S019 · 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。 - S018 · 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。 - S017 · 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。 - S016 · 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。 - S015 · 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。 - S014 · 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。 - S013 · 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。 - S012 · 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。 - 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, 11], 是, 是, 是, 是, center_is_a_subgroup_by_complete_identity_product_inverse_audit) 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: 523d285e7fe29b4c188a26af33cd9c21cfce31936354f1ff6d41465ba8943f92 - candidate record SHA-256: 77b60e90e691122e7b312b552ad39b0ae7786aaba3eecf003e8b5fd4d9b2064c - 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-r02-finite-group-center-0045.json)