# 第 25639 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-0014) 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。 R0050-25639 · q-20261015-advance-20261115-r02-finite-group-center-0014 ## 原題與已知條件 完整Cayley table上的forall-g commutation與center資格。操作=center-commutation-table；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],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,0,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,16],[2,3,4,5,6,7,8,9,10,11,12,13,14,15,0,1,18,19,20,21,22,23,24,25,26,27,28,29,30,31,16,17],[3,4,5,6,7,8,9,10,11,12,13,14,15,0,1,2,19,20,21,22,23,24,25,26,27,28,29,30,31,16,17,18],[4,5,6,7,8,9,10,11,12,13,14,15,0,1,2,3,20,21,22,23,24,25,26,27,28,29,30,31,16,17,18,19],[5,6,7,8,9,10,11,12,13,14,15,0,1,2,3,4,21,22,23,24,25,26,27,28,29,30,31,16,17,18,19,20],[6,7,8,9,10,11,12,13,14,15,0,1,2,3,4,5,22,23,24,25,26,27,28,29,30,31,16,17,18,19,20,21],[7,8,9,10,11,12,13,14,15,0,1,2,3,4,5,6,23,24,25,26,27,28,29,30,31,16,17,18,19,20,21,22],[8,9,10,11,12,13,14,15,0,1,2,3,4,5,6,7,24,25,26,27,28,29,30,31,16,17,18,19,20,21,22,23],[9,10,11,12,13,14,15,0,1,2,3,4,5,6,7,8,25,26,27,28,29,30,31,16,17,18,19,20,21,22,23,24],[10,11,12,13,14,15,0,1,2,3,4,5,6,7,8,9,26,27,28,29,30,31,16,17,18,19,20,21,22,23,24,25],[11,12,13,14,15,0,1,2,3,4,5,6,7,8,9,10,27,28,29,30,31,16,17,18,19,20,21,22,23,24,25,26],[12,13,14,15,0,1,2,3,4,5,6,7,8,9,10,11,28,29,30,31,16,17,18,19,20,21,22,23,24,25,26,27],[13,14,15,0,1,2,3,4,5,6,7,8,9,10,11,12,29,30,31,16,17,18,19,20,21,22,23,24,25,26,27,28],[14,15,0,1,2,3,4,5,6,7,8,9,10,11,12,13,30,31,16,17,18,19,20,21,22,23,24,25,26,27,28,29],[15,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,31,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30],[16,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,0,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1],[17,16,31,30,29,28,27,26,25,24,23,22,21,20,19,18,1,0,15,14,13,12,11,10,9,8,7,6,5,4,3,2],[18,17,16,31,30,29,28,27,26,25,24,23,22,21,20,19,2,1,0,15,14,13,12,11,10,9,8,7,6,5,4,3],[19,18,17,16,31,30,29,28,27,26,25,24,23,22,21,20,3,2,1,0,15,14,13,12,11,10,9,8,7,6,5,4],[20,19,18,17,16,31,30,29,28,27,26,25,24,23,22,21,4,3,2,1,0,15,14,13,12,11,10,9,8,7,6,5],[21,20,19,18,17,16,31,30,29,28,27,26,25,24,23,22,5,4,3,2,1,0,15,14,13,12,11,10,9,8,7,6],[22,21,20,19,18,17,16,31,30,29,28,27,26,25,24,23,6,5,4,3,2,1,0,15,14,13,12,11,10,9,8,7],[23,22,21,20,19,18,17,16,31,30,29,28,27,26,25,24,7,6,5,4,3,2,1,0,15,14,13,12,11,10,9,8],[24,23,22,21,20,19,18,17,16,31,30,29,28,27,26,25,8,7,6,5,4,3,2,1,0,15,14,13,12,11,10,9],[25,24,23,22,21,20,19,18,17,16,31,30,29,28,27,26,9,8,7,6,5,4,3,2,1,0,15,14,13,12,11,10],[26,25,24,23,22,21,20,19,18,17,16,31,30,29,28,27,10,9,8,7,6,5,4,3,2,1,0,15,14,13,12,11],[27,26,25,24,23,22,21,20,19,18,17,16,31,30,29,28,11,10,9,8,7,6,5,4,3,2,1,0,15,14,13,12],[28,27,26,25,24,23,22,21,20,19,18,17,16,31,30,29,12,11,10,9,8,7,6,5,4,3,2,1,0,15,14,13],[29,28,27,26,25,24,23,22,21,20,19,18,17,16,31,30,13,12,11,10,9,8,7,6,5,4,3,2,1,0,15,14],[30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,31,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,15],[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-commutation-table；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],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,0,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,16],[2,3,4,5,6,7,8,9,10,11,12,13,14,15,0,1,18,19,20,21,22,23,24,25,26,27,28,29,30,31,16,17],[3,4,5,6,7,8,9,10,11,12,13,14,15,0,1,2,19,20,21,22,23,24,25,26,27,28,29,30,31,16,17,18],[4,5,6,7,8,9,10,11,12,13,14,15,0,1,2,3,20,21,22,23,24,25,26,27,28,29,30,31,16,17,18,19],[5,6,7,8,9,10,11,12,13,14,15,0,1,2,3,4,21,22,23,24,25,26,27,28,29,30,31,16,17,18,19,20],[6,7,8,9,10,11,12,13,14,15,0,1,2,3,4,5,22,23,24,25,26,27,28,29,30,31,16,17,18,19,20,21],[7,8,9,10,11,12,13,14,15,0,1,2,3,4,5,6,23,24,25,26,27,28,29,30,31,16,17,18,19,20,21,22],[8,9,10,11,12,13,14,15,0,1,2,3,4,5,6,7,24,25,26,27,28,29,30,31,16,17,18,19,20,21,22,23],[9,10,11,12,13,14,15,0,1,2,3,4,5,6,7,8,25,26,27,28,29,30,31,16,17,18,19,20,21,22,23,24],[10,11,12,13,14,15,0,1,2,3,4,5,6,7,8,9,26,27,28,29,30,31,16,17,18,19,20,21,22,23,24,25],[11,12,13,14,15,0,1,2,3,4,5,6,7,8,9,10,27,28,29,30,31,16,17,18,19,20,21,22,23,24,25,26],[12,13,14,15,0,1,2,3,4,5,6,7,8,9,10,11,28,29,30,31,16,17,18,19,20,21,22,23,24,25,26,27],[13,14,15,0,1,2,3,4,5,6,7,8,9,10,11,12,29,30,31,16,17,18,19,20,21,22,23,24,25,26,27,28],[14,15,0,1,2,3,4,5,6,7,8,9,10,11,12,13,30,31,16,17,18,19,20,21,22,23,24,25,26,27,28,29],[15,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,31,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30],[16,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,0,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1],[17,16,31,30,29,28,27,26,25,24,23,22,21,20,19,18,1,0,15,14,13,12,11,10,9,8,7,6,5,4,3,2],[18,17,16,31,30,29,28,27,26,25,24,23,22,21,20,19,2,1,0,15,14,13,12,11,10,9,8,7,6,5,4,3],[19,18,17,16,31,30,29,28,27,26,25,24,23,22,21,20,3,2,1,0,15,14,13,12,11,10,9,8,7,6,5,4],[20,19,18,17,16,31,30,29,28,27,26,25,24,23,22,21,4,3,2,1,0,15,14,13,12,11,10,9,8,7,6,5],[21,20,19,18,17,16,31,30,29,28,27,26,25,24,23,22,5,4,3,2,1,0,15,14,13,12,11,10,9,8,7,6],[22,21,20,19,18,17,16,31,30,29,28,27,26,25,24,23,6,5,4,3,2,1,0,15,14,13,12,11,10,9,8,7],[23,22,21,20,19,18,17,16,31,30,29,28,27,26,25,24,7,6,5,4,3,2,1,0,15,14,13,12,11,10,9,8],[24,23,22,21,20,19,18,17,16,31,30,29,28,27,26,25,8,7,6,5,4,3,2,1,0,15,14,13,12,11,10,9],[25,24,23,22,21,20,19,18,17,16,31,30,29,28,27,26,9,8,7,6,5,4,3,2,1,0,15,14,13,12,11,10],[26,25,24,23,22,21,20,19,18,17,16,31,30,29,28,27,10,9,8,7,6,5,4,3,2,1,0,15,14,13,12,11],[27,26,25,24,23,22,21,20,19,18,17,16,31,30,29,28,11,10,9,8,7,6,5,4,3,2,1,0,15,14,13,12],[28,27,26,25,24,23,22,21,20,19,18,17,16,31,30,29,12,11,10,9,8,7,6,5,4,3,2,1,0,15,14,13],[29,28,27,26,25,24,23,22,21,20,19,18,17,16,31,30,13,12,11,10,9,8,7,6,5,4,3,2,1,0,15,14],[30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,31,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,15],[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-commutation-table] 操作後 derived = [[commutation_rows, center, 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], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 0, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 16], [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 0, 1, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 16, 17], [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 0, 1, 2, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 16, 17, 18], [4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 0, 1, 2, 3, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 16, 17, 18, 19], [5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 0, 1, 2, 3, 4, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 16, 17, 18, 19, 20], [6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 0, 1, 2, 3, 4, 5, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 16, 17, 18, 19, 20, 21], [7, 8, 9, 10, 11, 12, 13, 14, 15, 0, 1, 2, 3, 4, 5, 6, 23, 24, 25, 26, 27, 28, 29, 30, 31, 16, 17, 18, 19, 20, 21, 22], [8, 9, 10, 11, 12, 13, 14, 15, 0, 1, 2, 3, 4, 5, 6, 7, 24, 25, 26, 27, 28, 29, 30, 31, 16, 17, 18, 19, 20, 21, 22, 23], [9, 10, 11, 12, 13, 14, 15, 0, 1, 2, 3, 4, 5, 6, 7, 8, 25, 26, 27, 28, 29, 30, 31, 16, 17, 18, 19, 20, 21, 22, 23, 24], [10, 11, 12, 13, 14, 15, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 26, 27, 28, 29, 30, 31, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25], [11, 12, 13, 14, 15, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 27, 28, 29, 30, 31, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26], [12, 13, 14, 15, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 28, 29, 30, 31, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27], [13, 14, 15, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 29, 30, 31, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28], [14, 15, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 30, 31, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29], [15, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 31, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30], [16, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 0, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1], [17, 16, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 1, 0, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2], [18, 17, 16, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 2, 1, 0, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3], [19, 18, 17, 16, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 3, 2, 1, 0, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4], [20, 19, 18, 17, 16, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 4, 3, 2, 1, 0, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5], [21, 20, 19, 18, 17, 16, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 5, 4, 3, 2, 1, 0, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6], [22, 21, 20, 19, 18, 17, 16, 31, 30, 29, 28, 27, 26, 25, 24, 23, 6, 5, 4, 3, 2, 1, 0, 15, 14, 13, 12, 11, 10, 9, 8, 7], [23, 22, 21, 20, 19, 18, 17, 16, 31, 30, 29, 28, 27, 26, 25, 24, 7, 6, 5, 4, 3, 2, 1, 0, 15, 14, 13, 12, 11, 10, 9, 8], [24, 23, 22, 21, 20, 19, 18, 17, 16, 31, 30, 29, 28, 27, 26, 25, 8, 7, 6, 5, 4, 3, 2, 1, 0, 15, 14, 13, 12, 11, 10, 9], [25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 31, 30, 29, 28, 27, 26, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 15, 14, 13, 12, 11, 10], [26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 31, 30, 29, 28, 27, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 15, 14, 13, 12, 11], [27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 31, 30, 29, 28, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 15, 14, 13, 12], [28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 31, 30, 29, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 15, 14, 13], [29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 31, 30, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 15, 14], [30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 31, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 15], [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 = [32, [[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]], 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, 32, 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, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是]], 32768, [0, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31]] 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]] 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], [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], [是, 是, 是, 是, 是, 是, 是, 是, 是, 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]] 操作後 derived = [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 0, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 16], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 0, 31, 16, 17, 18, 19, 20, 21, 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, 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]] 操作後 derived = [[2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 0, 1, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 16, 17], [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 0, 1, 30, 31, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29], [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] 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]] 操作後 derived = [[3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 0, 1, 2, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 16, 17, 18], [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 0, 1, 2, 29, 30, 31, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28], [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] 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]] 操作後 derived = [[4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 0, 1, 2, 3, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 16, 17, 18, 19], [4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 0, 1, 2, 3, 28, 29, 30, 31, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27], [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] 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]] 操作後 derived = [[5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 0, 1, 2, 3, 4, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 16, 17, 18, 19, 20], [5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 0, 1, 2, 3, 4, 27, 28, 29, 30, 31, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26], [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] 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]] 操作後 derived = [[6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 0, 1, 2, 3, 4, 5, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 16, 17, 18, 19, 20, 21], [6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 0, 1, 2, 3, 4, 5, 26, 27, 28, 29, 30, 31, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25], [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] 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]] 操作後 derived = [[7, 8, 9, 10, 11, 12, 13, 14, 15, 0, 1, 2, 3, 4, 5, 6, 23, 24, 25, 26, 27, 28, 29, 30, 31, 16, 17, 18, 19, 20, 21, 22], [7, 8, 9, 10, 11, 12, 13, 14, 15, 0, 1, 2, 3, 4, 5, 6, 25, 26, 27, 28, 29, 30, 31, 16, 17, 18, 19, 20, 21, 22, 23, 24], [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] 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]] 操作後 derived = [[8, 9, 10, 11, 12, 13, 14, 15, 0, 1, 2, 3, 4, 5, 6, 7, 24, 25, 26, 27, 28, 29, 30, 31, 16, 17, 18, 19, 20, 21, 22, 23], [8, 9, 10, 11, 12, 13, 14, 15, 0, 1, 2, 3, 4, 5, 6, 7, 24, 25, 26, 27, 28, 29, 30, 31, 16, 17, 18, 19, 20, 21, 22, 23], [是, 是, 是, 是, 是, 是, 是, 是, 是, 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, 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]] 操作後 derived = [[9, 10, 11, 12, 13, 14, 15, 0, 1, 2, 3, 4, 5, 6, 7, 8, 25, 26, 27, 28, 29, 30, 31, 16, 17, 18, 19, 20, 21, 22, 23, 24], [9, 10, 11, 12, 13, 14, 15, 0, 1, 2, 3, 4, 5, 6, 7, 8, 23, 24, 25, 26, 27, 28, 29, 30, 31, 16, 17, 18, 19, 20, 21, 22], [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] 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]] 操作後 derived = [[10, 11, 12, 13, 14, 15, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 26, 27, 28, 29, 30, 31, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25], [10, 11, 12, 13, 14, 15, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 16, 17, 18, 19, 20, 21], [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] 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]] 操作後 derived = [[11, 12, 13, 14, 15, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 27, 28, 29, 30, 31, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26], [11, 12, 13, 14, 15, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 16, 17, 18, 19, 20], [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] 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]] 操作後 derived = [[12, 13, 14, 15, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 28, 29, 30, 31, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27], [12, 13, 14, 15, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 16, 17, 18, 19], [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] 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]] 操作後 derived = [[13, 14, 15, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 29, 30, 31, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28], [13, 14, 15, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 16, 17, 18], [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] 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]] 操作後 derived = [[14, 15, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 30, 31, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29], [14, 15, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 16, 17], [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] 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]] 操作後 derived = [[15, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 31, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30], [15, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 16], [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] 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]] 操作後 derived = [[16, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 0, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1], [16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15], [是, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 是, 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, 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]] 操作後 derived = [[17, 16, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 1, 0, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2], [17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 16, 15, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14], [是, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 是, 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, 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]] 操作後 derived = [[18, 17, 16, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 2, 1, 0, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3], [18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 16, 17, 14, 15, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13], [是, 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, 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, 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]] 操作後 derived = [[19, 18, 17, 16, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 3, 2, 1, 0, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4], [19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 16, 17, 18, 13, 14, 15, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], [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, 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, 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]] 操作後 derived = [[20, 19, 18, 17, 16, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 4, 3, 2, 1, 0, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5], [20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 16, 17, 18, 19, 12, 13, 14, 15, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [是, 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, 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, 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]] 操作後 derived = [[21, 20, 19, 18, 17, 16, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 5, 4, 3, 2, 1, 0, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6], [21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 16, 17, 18, 19, 20, 11, 12, 13, 14, 15, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10], [是, 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, 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, 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]] 操作後 derived = [[22, 21, 20, 19, 18, 17, 16, 31, 30, 29, 28, 27, 26, 25, 24, 23, 6, 5, 4, 3, 2, 1, 0, 15, 14, 13, 12, 11, 10, 9, 8, 7], [22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 16, 17, 18, 19, 20, 21, 10, 11, 12, 13, 14, 15, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [是, 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, 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, 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]] 操作後 derived = [[23, 22, 21, 20, 19, 18, 17, 16, 31, 30, 29, 28, 27, 26, 25, 24, 7, 6, 5, 4, 3, 2, 1, 0, 15, 14, 13, 12, 11, 10, 9, 8], [23, 24, 25, 26, 27, 28, 29, 30, 31, 16, 17, 18, 19, 20, 21, 22, 9, 10, 11, 12, 13, 14, 15, 0, 1, 2, 3, 4, 5, 6, 7, 8], [是, 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, 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, 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]] 操作後 derived = [[24, 23, 22, 21, 20, 19, 18, 17, 16, 31, 30, 29, 28, 27, 26, 25, 8, 7, 6, 5, 4, 3, 2, 1, 0, 15, 14, 13, 12, 11, 10, 9], [24, 25, 26, 27, 28, 29, 30, 31, 16, 17, 18, 19, 20, 21, 22, 23, 8, 9, 10, 11, 12, 13, 14, 15, 0, 1, 2, 3, 4, 5, 6, 7], [是, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 是, 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, 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]] 操作後 derived = [[25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 31, 30, 29, 28, 27, 26, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 15, 14, 13, 12, 11, 10], [25, 26, 27, 28, 29, 30, 31, 16, 17, 18, 19, 20, 21, 22, 23, 24, 7, 8, 9, 10, 11, 12, 13, 14, 15, 0, 1, 2, 3, 4, 5, 6], [是, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 是, 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, 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]] 操作後 derived = [[26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 31, 30, 29, 28, 27, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 15, 14, 13, 12, 11], [26, 27, 28, 29, 30, 31, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 0, 1, 2, 3, 4, 5], [是, 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, 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, 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]] 操作後 derived = [[27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 31, 30, 29, 28, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 15, 14, 13, 12], [27, 28, 29, 30, 31, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 0, 1, 2, 3, 4], [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, 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, 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]] 操作後 derived = [[28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 31, 30, 29, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 15, 14, 13], [28, 29, 30, 31, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 0, 1, 2, 3], [是, 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, 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, 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]] 操作後 derived = [[29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 31, 30, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 15, 14], [29, 30, 31, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 0, 1, 2], [是, 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, 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, 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]] 操作後 derived = [[30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 31, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 15], [30, 31, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 0, 1], [是, 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, 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, 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]] 操作後 derived = [[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], [31, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 0], [是, 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, 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, S034 S036 · implies操作前 source roles = [Center ACTUAL Z, [0, 8], 0] 操作後 derived = [是, [[0, 0, 0, 是], [0, 8, 8, 是], [8, 0, 8, 是], [8, 8, 0, 是]], 是, [[0, 0, 是], [8, 8, 是]], 是, 是, [[0, [0, 8], 是], [1, [0, 8], 是], [2, [0, 8], 是], [3, [0, 8], 是], [4, [0, 8], 是], [5, [0, 8], 是], [6, [0, 8], 是], [7, [0, 8], 是], [8, [0, 8], 是], [9, [0, 8], 是], [10, [0, 8], 是], [11, [0, 8], 是], [12, [0, 8], 是], [13, [0, 8], 是], [14, [0, 8], 是], [15, [0, 8], 是], [16, [0, 8], 是], [17, [0, 8], 是], [18, [0, 8], 是], [19, [0, 8], 是], [20, [0, 8], 是], [21, [0, 8], 是], [22, [0, 8], 是], [23, [0, 8], 是], [24, [0, 8], 是], [25, [0, 8], 是], [26, [0, 8], 是], [27, [0, 8], 是], [28, [0, 8], 是], [29, [0, 8], 是], [30, [0, 8], 是], [31, [0, 8], 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, S035 S037 · implies操作前 source roles = [[0, 8], [[是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 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], [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], [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], [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], [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], [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], [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], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 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], [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], [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], [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], [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], [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], [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], [是, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否], [是, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否], [是, 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, 是, 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, 是, 否, 否, 否, 否], [是, 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, 是, 否, 否, 否], [是, 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, 是, 否, 否], [是, 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, 是, 否], [是, 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, 是], [是, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否], [是, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否], [是, 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, 是, 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, 是, 否, 否, 否, 否], [是, 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, 是, 否, 否, 否], [是, 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, 是, 否, 否], [是, 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, 是, 否], [是, 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, 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, S036 ## 逐步反向核對 - 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, [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是]], [1, [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]], [2, [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]], [3, [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]], [4, [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]], [5, [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]], [6, [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]], [7, [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]], [8, [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是]], [9, [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]], [10, [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]], [11, [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]], [12, [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]], [13, [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]], [14, [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]], [15, [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]], [16, [是, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否]], [17, [是, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否]], [18, [是, 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, 是, 否, 否, 否, 否, 否]], [19, [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, 是, 否, 否, 否, 否]], [20, [是, 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, 是, 否, 否, 否]], [21, [是, 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, 是, 否, 否]], [22, [是, 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, 是, 否]], [23, [是, 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, 是]], [24, [是, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否]], [25, [是, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否]], [26, [是, 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, 是, 否, 否, 否, 否, 否]], [27, [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, 是, 否, 否, 否, 否]], [28, [是, 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, 是, 否, 否, 否]], [29, [是, 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, 是, 否, 否]], [30, [是, 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, 是, 否]], [31, [是, 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, 是]]], [0, 8], Z_G_contains_exactly_the_elements_commuting_with_every_g) 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: 8ce864709b33fa29aba94829e622a2e33988a841fc136f745a2301ae2e551f54 - candidate record SHA-256: 4509427fc87ef7b5baf5a2db24600eb7c814e0a4215c0f6b8cfde28d6ff2d21c - 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-0014.json)