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第 25616 題：有限群中心

本頁導覽
  1. 原題與已知條件
  2. 定義與適用範圍
  3. 逐步推導
  4. 逐步反向核對
  5. 結論
  6. 本題覆核與來源綁定

返回所在分頁 129

← 逐題詳解目錄 · 原題批次

R0050-25616 · q-20261015-advance-20261115-r02-finite-group-center-0091

原題與已知條件

完整Cayley table上的forall-g commutation與center資格。操作=center-abelian-conjugacy-boundary；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],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,0,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,18],[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,0,1,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,18,19],[3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,0,1,2,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,18,19,20],[4,5,6,7,8,9,10,11,12,13,14,15,16,17,0,1,2,3,22,23,24,25,26,27,28,29,30,31,32,33,34,35,18,19,20,21],[5,6,7,8,9,10,11,12,13,14,15,16,17,0,1,2,3,4,23,24,25,26,27,28,29,30,31,32,33,34,35,18,19,20,21,22],[6,7,8,9,10,11,12,13,14,15,16,17,0,1,2,3,4,5,24,25,26,27,28,29,30,31,32,33,34,35,18,19,20,21,22,23],[7,8,9,10,11,12,13,14,15,16,17,0,1,2,3,4,5,6,25,26,27,28,29,30,31,32,33,34,35,18,19,20,21,22,23,24],[8,9,10,11,12,13,14,15,16,17,0,1,2,3,4,5,6,7,26,27,28,29,30,31,32,33,34,35,18,19,20,21,22,23,24,25],[9,10,11,12,13,14,15,16,17,0,1,2,3,4,5,6,7,8,27,28,29,30,31,32,33,34,35,18,19,20,21,22,23,24,25,26],[10,11,12,13,14,15,16,17,0,1,2,3,4,5,6,7,8,9,28,29,30,31,32,33,34,35,18,19,20,21,22,23,24,25,26,27],[11,12,13,14,15,16,17,0,1,2,3,4,5,6,7,8,9,10,29,30,31,32,33,34,35,18,19,20,21,22,23,24,25,26,27,28],[12,13,14,15,16,17,0,1,2,3,4,5,6,7,8,9,10,11,30,31,32,33,34,35,18,19,20,21,22,23,24,25,26,27,28,29],[13,14,15,16,17,0,1,2,3,4,5,6,7,8,9,10,11,12,31,32,33,34,35,18,19,20,21,22,23,24,25,26,27,28,29,30],[14,15,16,17,0,1,2,3,4,5,6,7,8,9,10,11,12,13,32,33,34,35,18,19,20,21,22,23,24,25,26,27,28,29,30,31],[15,16,17,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,33,34,35,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32],[16,17,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,34,35,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33],[17,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,35,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34],[18,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,0,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1],[19,18,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,1,0,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2],[20,19,18,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,2,1,0,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3],[21,20,19,18,35,34,33,32,31,30,29,28,27,26,25,24,23,22,3,2,1,0,17,16,15,14,13,12,11,10,9,8,7,6,5,4],[22,21,20,19,18,35,34,33,32,31,30,29,28,27,26,25,24,23,4,3,2,1,0,17,16,15,14,13,12,11,10,9,8,7,6,5],[23,22,21,20,19,18,35,34,33,32,31,30,29,28,27,26,25,24,5,4,3,2,1,0,17,16,15,14,13,12,11,10,9,8,7,6],[24,23,22,21,20,19,18,35,34,33,32,31,30,29,28,27,26,25,6,5,4,3,2,1,0,17,16,15,14,13,12,11,10,9,8,7],[25,24,23,22,21,20,19,18,35,34,33,32,31,30,29,28,27,26,7,6,5,4,3,2,1,0,17,16,15,14,13,12,11,10,9,8],[26,25,24,23,22,21,20,19,18,35,34,33,32,31,30,29,28,27,8,7,6,5,4,3,2,1,0,17,16,15,14,13,12,11,10,9],[27,26,25,24,23,22,21,20,19,18,35,34,33,32,31,30,29,28,9,8,7,6,5,4,3,2,1,0,17,16,15,14,13,12,11,10],[28,27,26,25,24,23,22,21,20,19,18,35,34,33,32,31,30,29,10,9,8,7,6,5,4,3,2,1,0,17,16,15,14,13,12,11],[29,28,27,26,25,24,23,22,21,20,19,18,35,34,33,32,31,30,11,10,9,8,7,6,5,4,3,2,1,0,17,16,15,14,13,12],[30,29,28,27,26,25,24,23,22,21,20,19,18,35,34,33,32,31,12,11,10,9,8,7,6,5,4,3,2,1,0,17,16,15,14,13],[31,30,29,28,27,26,25,24,23,22,21,20,19,18,35,34,33,32,13,12,11,10,9,8,7,6,5,4,3,2,1,0,17,16,15,14],[32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,35,34,33,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,17,16,15],[33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,35,34,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,17,16],[34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,35,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,17],[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,"element":9}。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-abelian-conjugacy-boundary；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],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,0,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,18],[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,0,1,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,18,19],[3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,0,1,2,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,18,19,20],[4,5,6,7,8,9,10,11,12,13,14,15,16,17,0,1,2,3,22,23,24,25,26,27,28,29,30,31,32,33,34,35,18,19,20,21],[5,6,7,8,9,10,11,12,13,14,15,16,17,0,1,2,3,4,23,24,25,26,27,28,29,30,31,32,33,34,35,18,19,20,21,22],[6,7,8,9,10,11,12,13,14,15,16,17,0,1,2,3,4,5,24,25,26,27,28,29,30,31,32,33,34,35,18,19,20,21,22,23],[7,8,9,10,11,12,13,14,15,16,17,0,1,2,3,4,5,6,25,26,27,28,29,30,31,32,33,34,35,18,19,20,21,22,23,24],[8,9,10,11,12,13,14,15,16,17,0,1,2,3,4,5,6,7,26,27,28,29,30,31,32,33,34,35,18,19,20,21,22,23,24,25],[9,10,11,12,13,14,15,16,17,0,1,2,3,4,5,6,7,8,27,28,29,30,31,32,33,34,35,18,19,20,21,22,23,24,25,26],[10,11,12,13,14,15,16,17,0,1,2,3,4,5,6,7,8,9,28,29,30,31,32,33,34,35,18,19,20,21,22,23,24,25,26,27],[11,12,13,14,15,16,17,0,1,2,3,4,5,6,7,8,9,10,29,30,31,32,33,34,35,18,19,20,21,22,23,24,25,26,27,28],[12,13,14,15,16,17,0,1,2,3,4,5,6,7,8,9,10,11,30,31,32,33,34,35,18,19,20,21,22,23,24,25,26,27,28,29],[13,14,15,16,17,0,1,2,3,4,5,6,7,8,9,10,11,12,31,32,33,34,35,18,19,20,21,22,23,24,25,26,27,28,29,30],[14,15,16,17,0,1,2,3,4,5,6,7,8,9,10,11,12,13,32,33,34,35,18,19,20,21,22,23,24,25,26,27,28,29,30,31],[15,16,17,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,33,34,35,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32],[16,17,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,34,35,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33],[17,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,35,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34],[18,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,0,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1],[19,18,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,1,0,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2],[20,19,18,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,2,1,0,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3],[21,20,19,18,35,34,33,32,31,30,29,28,27,26,25,24,23,22,3,2,1,0,17,16,15,14,13,12,11,10,9,8,7,6,5,4],[22,21,20,19,18,35,34,33,32,31,30,29,28,27,26,25,24,23,4,3,2,1,0,17,16,15,14,13,12,11,10,9,8,7,6,5],[23,22,21,20,19,18,35,34,33,32,31,30,29,28,27,26,25,24,5,4,3,2,1,0,17,16,15,14,13,12,11,10,9,8,7,6],[24,23,22,21,20,19,18,35,34,33,32,31,30,29,28,27,26,25,6,5,4,3,2,1,0,17,16,15,14,13,12,11,10,9,8,7],[25,24,23,22,21,20,19,18,35,34,33,32,31,30,29,28,27,26,7,6,5,4,3,2,1,0,17,16,15,14,13,12,11,10,9,8],[26,25,24,23,22,21,20,19,18,35,34,33,32,31,30,29,28,27,8,7,6,5,4,3,2,1,0,17,16,15,14,13,12,11,10,9],[27,26,25,24,23,22,21,20,19,18,35,34,33,32,31,30,29,28,9,8,7,6,5,4,3,2,1,0,17,16,15,14,13,12,11,10],[28,27,26,25,24,23,22,21,20,19,18,35,34,33,32,31,30,29,10,9,8,7,6,5,4,3,2,1,0,17,16,15,14,13,12,11],[29,28,27,26,25,24,23,22,21,20,19,18,35,34,33,32,31,30,11,10,9,8,7,6,5,4,3,2,1,0,17,16,15,14,13,12],[30,29,28,27,26,25,24,23,22,21,20,19,18,35,34,33,32,31,12,11,10,9,8,7,6,5,4,3,2,1,0,17,16,15,14,13],[31,30,29,28,27,26,25,24,23,22,21,20,19,18,35,34,33,32,13,12,11,10,9,8,7,6,5,4,3,2,1,0,17,16,15,14],[32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,35,34,33,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,17,16,15],[33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,35,34,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,17,16],[34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,35,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,17],[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,"element":9}。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。

逐步推導

S001 · implies

操作前

source roles = [center-abelian-conjugacy-boundary]

操作後

derived = [[element, central, conjugacy_class, singleton_class, central_singleton_equivalence, center, abelian, center_equals_group, abelian_center_equivalence, noncommuting_element_or_null, boundary]]

條件：無

直接列完整來源欄序，不需JavaScript。LP weak為13欄、zero與strong為15欄，前提與角色依原operation／mode，不補欄。

步驟識別與依賴

規則：source_ordered_fields_without_JS · 依賴：G001

S002 · implies

操作前

source roles = [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], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 0, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 18], [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 0, 1, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 18, 19], [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 0, 1, 2, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 18, 19, 20], [4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 0, 1, 2, 3, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 18, 19, 20, 21], [5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 0, 1, 2, 3, 4, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 18, 19, 20, 21, 22], [6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 0, 1, 2, 3, 4, 5, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 18, 19, 20, 21, 22, 23], [7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 0, 1, 2, 3, 4, 5, 6, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 18, 19, 20, 21, 22, 23, 24], [8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 0, 1, 2, 3, 4, 5, 6, 7, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 18, 19, 20, 21, 22, 23, 24, 25], [9, 10, 11, 12, 13, 14, 15, 16, 17, 0, 1, 2, 3, 4, 5, 6, 7, 8, 27, 28, 29, 30, 31, 32, 33, 34, 35, 18, 19, 20, 21, 22, 23, 24, 25, 26], [10, 11, 12, 13, 14, 15, 16, 17, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 28, 29, 30, 31, 32, 33, 34, 35, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27], [11, 12, 13, 14, 15, 16, 17, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 29, 30, 31, 32, 33, 34, 35, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28], [12, 13, 14, 15, 16, 17, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 30, 31, 32, 33, 34, 35, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29], [13, 14, 15, 16, 17, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 31, 32, 33, 34, 35, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30], [14, 15, 16, 17, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 32, 33, 34, 35, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31], [15, 16, 17, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 33, 34, 35, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32], [16, 17, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 34, 35, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33], [17, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 35, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34], [18, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 0, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1], [19, 18, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 1, 0, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2], [20, 19, 18, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 2, 1, 0, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3], [21, 20, 19, 18, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 3, 2, 1, 0, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4], [22, 21, 20, 19, 18, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 4, 3, 2, 1, 0, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5], [23, 22, 21, 20, 19, 18, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 5, 4, 3, 2, 1, 0, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6], [24, 23, 22, 21, 20, 19, 18, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 6, 5, 4, 3, 2, 1, 0, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7], [25, 24, 23, 22, 21, 20, 19, 18, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 7, 6, 5, 4, 3, 2, 1, 0, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8], [26, 25, 24, 23, 22, 21, 20, 19, 18, 35, 34, 33, 32, 31, 30, 29, 28, 27, 8, 7, 6, 5, 4, 3, 2, 1, 0, 17, 16, 15, 14, 13, 12, 11, 10, 9], [27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 35, 34, 33, 32, 31, 30, 29, 28, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 17, 16, 15, 14, 13, 12, 11, 10], [28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 35, 34, 33, 32, 31, 30, 29, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 17, 16, 15, 14, 13, 12, 11], [29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 35, 34, 33, 32, 31, 30, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 17, 16, 15, 14, 13, 12], [30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 35, 34, 33, 32, 31, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 17, 16, 15, 14, 13], [31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 35, 34, 33, 32, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 17, 16, 15, 14], [32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 35, 34, 33, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 17, 16, 15], [33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 35, 34, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 17, 16], [34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 35, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 17], [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 = [36, [[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]], 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, 36, 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, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是]], 46656, [0, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35]]

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]]

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], [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], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 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]]

操作後

derived = [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 0, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 18], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 0, 35, 18, 19, 20, 21, 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, 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]]

操作後

derived = [[2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 0, 1, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 18, 19], [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 0, 1, 34, 35, 18, 19, 20, 21, 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, 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]]

操作後

derived = [[3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 0, 1, 2, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 18, 19, 20], [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 0, 1, 2, 33, 34, 35, 18, 19, 20, 21, 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, 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]]

操作後

derived = [[4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 0, 1, 2, 3, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 18, 19, 20, 21], [4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 0, 1, 2, 3, 32, 33, 34, 35, 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, 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]]

操作後

derived = [[5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 0, 1, 2, 3, 4, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 18, 19, 20, 21, 22], [5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 0, 1, 2, 3, 4, 31, 32, 33, 34, 35, 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, 是, 是, 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]]

操作後

derived = [[6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 0, 1, 2, 3, 4, 5, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 18, 19, 20, 21, 22, 23], [6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 0, 1, 2, 3, 4, 5, 30, 31, 32, 33, 34, 35, 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, 是, 是, 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]]

操作後

derived = [[7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 0, 1, 2, 3, 4, 5, 6, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 18, 19, 20, 21, 22, 23, 24], [7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 0, 1, 2, 3, 4, 5, 6, 29, 30, 31, 32, 33, 34, 35, 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, 是, 是, 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]]

操作後

derived = [[8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 0, 1, 2, 3, 4, 5, 6, 7, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 18, 19, 20, 21, 22, 23, 24, 25], [8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 0, 1, 2, 3, 4, 5, 6, 7, 28, 29, 30, 31, 32, 33, 34, 35, 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, 是, 是, 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]]

操作後

derived = [[9, 10, 11, 12, 13, 14, 15, 16, 17, 0, 1, 2, 3, 4, 5, 6, 7, 8, 27, 28, 29, 30, 31, 32, 33, 34, 35, 18, 19, 20, 21, 22, 23, 24, 25, 26], [9, 10, 11, 12, 13, 14, 15, 16, 17, 0, 1, 2, 3, 4, 5, 6, 7, 8, 27, 28, 29, 30, 31, 32, 33, 34, 35, 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, 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, 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]]

操作後

derived = [[10, 11, 12, 13, 14, 15, 16, 17, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 28, 29, 30, 31, 32, 33, 34, 35, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27], [10, 11, 12, 13, 14, 15, 16, 17, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 18, 19, 20, 21, 22, 23, 24, 25], [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]

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]]

操作後

derived = [[11, 12, 13, 14, 15, 16, 17, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 29, 30, 31, 32, 33, 34, 35, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28], [11, 12, 13, 14, 15, 16, 17, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 18, 19, 20, 21, 22, 23, 24], [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]

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]]

操作後

derived = [[12, 13, 14, 15, 16, 17, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 30, 31, 32, 33, 34, 35, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29], [12, 13, 14, 15, 16, 17, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 18, 19, 20, 21, 22, 23], [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]

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]]

操作後

derived = [[13, 14, 15, 16, 17, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 31, 32, 33, 34, 35, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30], [13, 14, 15, 16, 17, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 18, 19, 20, 21, 22], [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]

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]]

操作後

derived = [[14, 15, 16, 17, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 32, 33, 34, 35, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31], [14, 15, 16, 17, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 18, 19, 20, 21], [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]

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]]

操作後

derived = [[15, 16, 17, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 33, 34, 35, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32], [15, 16, 17, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 18, 19, 20], [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]

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]]

操作後

derived = [[16, 17, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 34, 35, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33], [16, 17, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 18, 19], [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]

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]]

操作後

derived = [[17, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 35, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34], [17, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 18], [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]

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]]

操作後

derived = [[18, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 0, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1], [18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 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, 是, 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]

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]]

操作後

derived = [[19, 18, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 1, 0, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2], [19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 18, 17, 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, 是, 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]

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]]

操作後

derived = [[20, 19, 18, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 2, 1, 0, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3], [20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 18, 19, 16, 17, 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, 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]

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]]

操作後

derived = [[21, 20, 19, 18, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 3, 2, 1, 0, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4], [21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 18, 19, 20, 15, 16, 17, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14], [是, 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, 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, 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]]

操作後

derived = [[22, 21, 20, 19, 18, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 4, 3, 2, 1, 0, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5], [22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 18, 19, 20, 21, 14, 15, 16, 17, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13], [是, 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, 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, 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]]

操作後

derived = [[23, 22, 21, 20, 19, 18, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 5, 4, 3, 2, 1, 0, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6], [23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 18, 19, 20, 21, 22, 13, 14, 15, 16, 17, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], [是, 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, 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, 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]]

操作後

derived = [[24, 23, 22, 21, 20, 19, 18, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 6, 5, 4, 3, 2, 1, 0, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7], [24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 18, 19, 20, 21, 22, 23, 12, 13, 14, 15, 16, 17, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [是, 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, 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, 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]]

操作後

derived = [[25, 24, 23, 22, 21, 20, 19, 18, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 7, 6, 5, 4, 3, 2, 1, 0, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8], [25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 18, 19, 20, 21, 22, 23, 24, 11, 12, 13, 14, 15, 16, 17, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10], [是, 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, 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, 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]]

操作後

derived = [[26, 25, 24, 23, 22, 21, 20, 19, 18, 35, 34, 33, 32, 31, 30, 29, 28, 27, 8, 7, 6, 5, 4, 3, 2, 1, 0, 17, 16, 15, 14, 13, 12, 11, 10, 9], [26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 18, 19, 20, 21, 22, 23, 24, 25, 10, 11, 12, 13, 14, 15, 16, 17, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [是, 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, 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, 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]]

操作後

derived = [[27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 35, 34, 33, 32, 31, 30, 29, 28, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 17, 16, 15, 14, 13, 12, 11, 10], [27, 28, 29, 30, 31, 32, 33, 34, 35, 18, 19, 20, 21, 22, 23, 24, 25, 26, 9, 10, 11, 12, 13, 14, 15, 16, 17, 0, 1, 2, 3, 4, 5, 6, 7, 8], [是, 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, 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, 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]]

操作後

derived = [[28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 35, 34, 33, 32, 31, 30, 29, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 17, 16, 15, 14, 13, 12, 11], [28, 29, 30, 31, 32, 33, 34, 35, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 0, 1, 2, 3, 4, 5, 6, 7], [是, 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, 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, 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]]

操作後

derived = [[29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 35, 34, 33, 32, 31, 30, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 17, 16, 15, 14, 13, 12], [29, 30, 31, 32, 33, 34, 35, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 0, 1, 2, 3, 4, 5, 6], [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, 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, 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]]

操作後

derived = [[30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 35, 34, 33, 32, 31, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 17, 16, 15, 14, 13], [30, 31, 32, 33, 34, 35, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 0, 1, 2, 3, 4, 5], [是, 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, 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, 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]]

操作後

derived = [[31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 35, 34, 33, 32, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 17, 16, 15, 14], [31, 32, 33, 34, 35, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 0, 1, 2, 3, 4], [是, 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, 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, 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]]

操作後

derived = [[32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 35, 34, 33, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 17, 16, 15], [32, 33, 34, 35, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 0, 1, 2, 3], [是, 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, 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, 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]]

操作後

derived = [[33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 35, 34, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 17, 16], [33, 34, 35, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 0, 1, 2], [是, 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, 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, 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]]

操作後

derived = [[34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 35, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 17], [34, 35, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 0, 1], [是, 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, 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, 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]]

操作後

derived = [[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], [35, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 0], [是, 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, 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, S038

S040 · implies

操作前

source roles = [Center ACTUAL Z, [0, 9], 0]

操作後

derived = [是, [[0, 0, 0, 是], [0, 9, 9, 是], [9, 0, 9, 是], [9, 9, 0, 是]], 是, [[0, 0, 是], [9, 9, 是]], 是, 是, [[0, [0, 9], 是], [1, [0, 9], 是], [2, [0, 9], 是], [3, [0, 9], 是], [4, [0, 9], 是], [5, [0, 9], 是], [6, [0, 9], 是], [7, [0, 9], 是], [8, [0, 9], 是], [9, [0, 9], 是], [10, [0, 9], 是], [11, [0, 9], 是], [12, [0, 9], 是], [13, [0, 9], 是], [14, [0, 9], 是], [15, [0, 9], 是], [16, [0, 9], 是], [17, [0, 9], 是], [18, [0, 9], 是], [19, [0, 9], 是], [20, [0, 9], 是], [21, [0, 9], 是], [22, [0, 9], 是], [23, [0, 9], 是], [24, [0, 9], 是], [25, [0, 9], 是], [26, [0, 9], 是], [27, [0, 9], 是], [28, [0, 9], 是], [29, [0, 9], 是], [30, [0, 9], 是], [31, [0, 9], 是], [32, [0, 9], 是], [33, [0, 9], 是], [34, [0, 9], 是], [35, [0, 9], 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, S039

S041 · implies

操作前

source roles = [[0, 9], [[是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 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], [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], [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], [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], [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], [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], [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], [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], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 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], [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], [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], [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], [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], [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], [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], [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], [是, 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, 是, 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, 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, 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], [是, 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, 是, 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, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否], [是, 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, 是, 否, 否, 否], [是, 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, 是, 否, 否], [是, 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, 是, 否], [是, 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, 是], [是, 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, 是, 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, 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, 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], [是, 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, 是, 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, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否], [是, 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, 是, 否, 否, 否], [是, 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, 是, 否, 否], [是, 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, 是, 否], [是, 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, 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, S040

S042 · implies

操作前

source roles = [9, [[0, 9], [1, 9], [2, 9], [3, 9], [4, 9], [5, 9], [6, 9], [7, 9], [8, 9], [9, 9], [10, 9], [11, 9], [12, 9], [13, 9], [14, 9], [15, 9], [16, 9], [17, 9], [18, 9], [19, 9], [20, 9], [21, 9], [22, 9], [23, 9], [24, 9], [25, 9], [26, 9], [27, 9], [28, 9], [29, 9], [30, 9], [31, 9], [32, 9], [33, 9], [34, 9], [35, 9]], [0, 9]]

操作後

derived = [是, [9], 是, 是, 否, 否, 是, null]

條件：無

gxg^-1=x iff gx=xg，故central iff singleton；Z=G iff所有元素兩兩交換。兩條件都False時iff仍True；非central保原index首noncommuter，central給null，不混0／False。

步驟識別與依賴

規則：Center_actual_singleton_iff_and_abelian_iff_FLAGS_FIRST_noncommuter · 依賴：G001, S041

逐步反向核對

  • 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

(9, 是, [9], 是, 是, [0, 9], 否, 否, 是, null, center_is_not_a_single_element_centralizer_and_no_class_equation_or_characteristic_claim)

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: 51b1bf970f65fb8bfd1c0caa4b606cad1b4ca7f4054eee5faebfb10a17d004a9
  • candidate record SHA-256: 2e26ca58e4c04434d375eedb7ae95f711a9dff53f8845f30a7deb4f16a5de02c
  • semantic review receipt SHA-256: 74c63a2c12285a3b2073f8d9f102bc2ba5fb7ed890c5b7c3b8afa94f032eda82
  • question-first witness SHA-256: 6d56428610f8e86c45fd00a2ad3b27ad9c052956946f0b91d71a68536f79d95f
  • Lean: NOT_RUN · human review: NOT_PERFORMED
同源完整 JSON