第 25660 題：有限群中心

原題與已知條件

完整Cayley table上的forall-g commutation與center資格。操作=center-normality-audit；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23],[1,2,3,4,5,6,7,8,9,10,11,0,13,14,15,16,17,18,19,20,21,22,23,12],[2,3,4,5,6,7,8,9,10,11,0,1,14,15,16,17,18,19,20,21,22,23,12,13],[3,4,5,6,7,8,9,10,11,0,1,2,15,16,17,18,19,20,21,22,23,12,13,14],[4,5,6,7,8,9,10,11,0,1,2,3,16,17,18,19,20,21,22,23,12,13,14,15],[5,6,7,8,9,10,11,0,1,2,3,4,17,18,19,20,21,22,23,12,13,14,15,16],[6,7,8,9,10,11,0,1,2,3,4,5,18,19,20,21,22,23,12,13,14,15,16,17],[7,8,9,10,11,0,1,2,3,4,5,6,19,20,21,22,23,12,13,14,15,16,17,18],[8,9,10,11,0,1,2,3,4,5,6,7,20,21,22,23,12,13,14,15,16,17,18,19],[9,10,11,0,1,2,3,4,5,6,7,8,21,22,23,12,13,14,15,16,17,18,19,20],[10,11,0,1,2,3,4,5,6,7,8,9,22,23,12,13,14,15,16,17,18,19,20,21],[11,0,1,2,3,4,5,6,7,8,9,10,23,12,13,14,15,16,17,18,19,20,21,22],[12,23,22,21,20,19,18,17,16,15,14,13,0,11,10,9,8,7,6,5,4,3,2,1],[13,12,23,22,21,20,19,18,17,16,15,14,1,0,11,10,9,8,7,6,5,4,3,2],[14,13,12,23,22,21,20,19,18,17,16,15,2,1,0,11,10,9,8,7,6,5,4,3],[15,14,13,12,23,22,21,20,19,18,17,16,3,2,1,0,11,10,9,8,7,6,5,4],[16,15,14,13,12,23,22,21,20,19,18,17,4,3,2,1,0,11,10,9,8,7,6,5],[17,16,15,14,13,12,23,22,21,20,19,18,5,4,3,2,1,0,11,10,9,8,7,6],[18,17,16,15,14,13,12,23,22,21,20,19,6,5,4,3,2,1,0,11,10,9,8,7],[19,18,17,16,15,14,13,12,23,22,21,20,7,6,5,4,3,2,1,0,11,10,9,8],[20,19,18,17,16,15,14,13,12,23,22,21,8,7,6,5,4,3,2,1,0,11,10,9],[21,20,19,18,17,16,15,14,13,12,23,22,9,8,7,6,5,4,3,2,1,0,11,10],[22,21,20,19,18,17,16,15,14,13,12,23,10,9,8,7,6,5,4,3,2,1,0,11],[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-normality-audit；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23],[1,2,3,4,5,6,7,8,9,10,11,0,13,14,15,16,17,18,19,20,21,22,23,12],[2,3,4,5,6,7,8,9,10,11,0,1,14,15,16,17,18,19,20,21,22,23,12,13],[3,4,5,6,7,8,9,10,11,0,1,2,15,16,17,18,19,20,21,22,23,12,13,14],[4,5,6,7,8,9,10,11,0,1,2,3,16,17,18,19,20,21,22,23,12,13,14,15],[5,6,7,8,9,10,11,0,1,2,3,4,17,18,19,20,21,22,23,12,13,14,15,16],[6,7,8,9,10,11,0,1,2,3,4,5,18,19,20,21,22,23,12,13,14,15,16,17],[7,8,9,10,11,0,1,2,3,4,5,6,19,20,21,22,23,12,13,14,15,16,17,18],[8,9,10,11,0,1,2,3,4,5,6,7,20,21,22,23,12,13,14,15,16,17,18,19],[9,10,11,0,1,2,3,4,5,6,7,8,21,22,23,12,13,14,15,16,17,18,19,20],[10,11,0,1,2,3,4,5,6,7,8,9,22,23,12,13,14,15,16,17,18,19,20,21],[11,0,1,2,3,4,5,6,7,8,9,10,23,12,13,14,15,16,17,18,19,20,21,22],[12,23,22,21,20,19,18,17,16,15,14,13,0,11,10,9,8,7,6,5,4,3,2,1],[13,12,23,22,21,20,19,18,17,16,15,14,1,0,11,10,9,8,7,6,5,4,3,2],[14,13,12,23,22,21,20,19,18,17,16,15,2,1,0,11,10,9,8,7,6,5,4,3],[15,14,13,12,23,22,21,20,19,18,17,16,3,2,1,0,11,10,9,8,7,6,5,4],[16,15,14,13,12,23,22,21,20,19,18,17,4,3,2,1,0,11,10,9,8,7,6,5],[17,16,15,14,13,12,23,22,21,20,19,18,5,4,3,2,1,0,11,10,9,8,7,6],[18,17,16,15,14,13,12,23,22,21,20,19,6,5,4,3,2,1,0,11,10,9,8,7],[19,18,17,16,15,14,13,12,23,22,21,20,7,6,5,4,3,2,1,0,11,10,9,8],[20,19,18,17,16,15,14,13,12,23,22,21,8,7,6,5,4,3,2,1,0,11,10,9],[21,20,19,18,17,16,15,14,13,12,23,22,9,8,7,6,5,4,3,2,1,0,11,10],[22,21,20,19,18,17,16,15,14,13,12,23,10,9,8,7,6,5,4,3,2,1,0,11],[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

逐步推導

source roles = [center-normality-audit]

derived = [[center, conjugate_rows, normal, certificate]]

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], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 0, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 12], [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 0, 1, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 12, 13], [3, 4, 5, 6, 7, 8, 9, 10, 11, 0, 1, 2, 15, 16, 17, 18, 19, 20, 21, 22, 23, 12, 13, 14], [4, 5, 6, 7, 8, 9, 10, 11, 0, 1, 2, 3, 16, 17, 18, 19, 20, 21, 22, 23, 12, 13, 14, 15], [5, 6, 7, 8, 9, 10, 11, 0, 1, 2, 3, 4, 17, 18, 19, 20, 21, 22, 23, 12, 13, 14, 15, 16], [6, 7, 8, 9, 10, 11, 0, 1, 2, 3, 4, 5, 18, 19, 20, 21, 22, 23, 12, 13, 14, 15, 16, 17], [7, 8, 9, 10, 11, 0, 1, 2, 3, 4, 5, 6, 19, 20, 21, 22, 23, 12, 13, 14, 15, 16, 17, 18], [8, 9, 10, 11, 0, 1, 2, 3, 4, 5, 6, 7, 20, 21, 22, 23, 12, 13, 14, 15, 16, 17, 18, 19], [9, 10, 11, 0, 1, 2, 3, 4, 5, 6, 7, 8, 21, 22, 23, 12, 13, 14, 15, 16, 17, 18, 19, 20], [10, 11, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 22, 23, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21], [11, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 23, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22], [12, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 0, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1], [13, 12, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 1, 0, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2], [14, 13, 12, 23, 22, 21, 20, 19, 18, 17, 16, 15, 2, 1, 0, 11, 10, 9, 8, 7, 6, 5, 4, 3], [15, 14, 13, 12, 23, 22, 21, 20, 19, 18, 17, 16, 3, 2, 1, 0, 11, 10, 9, 8, 7, 6, 5, 4], [16, 15, 14, 13, 12, 23, 22, 21, 20, 19, 18, 17, 4, 3, 2, 1, 0, 11, 10, 9, 8, 7, 6, 5], [17, 16, 15, 14, 13, 12, 23, 22, 21, 20, 19, 18, 5, 4, 3, 2, 1, 0, 11, 10, 9, 8, 7, 6], [18, 17, 16, 15, 14, 13, 12, 23, 22, 21, 20, 19, 6, 5, 4, 3, 2, 1, 0, 11, 10, 9, 8, 7], [19, 18, 17, 16, 15, 14, 13, 12, 23, 22, 21, 20, 7, 6, 5, 4, 3, 2, 1, 0, 11, 10, 9, 8], [20, 19, 18, 17, 16, 15, 14, 13, 12, 23, 22, 21, 8, 7, 6, 5, 4, 3, 2, 1, 0, 11, 10, 9], [21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 23, 22, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 11, 10], [22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 23, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 11], [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]

derived = [24, [[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]], 是]

source roles = [Center ORIGINAL group, 24, 0]

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]], 13824, [0, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23]]

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]]

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], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 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]

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]]

derived = [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 0, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 12], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 0, 23, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22], [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]

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]]

derived = [[2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 0, 1, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 12, 13], [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 0, 1, 22, 23, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21], [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]

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]]

derived = [[3, 4, 5, 6, 7, 8, 9, 10, 11, 0, 1, 2, 15, 16, 17, 18, 19, 20, 21, 22, 23, 12, 13, 14], [3, 4, 5, 6, 7, 8, 9, 10, 11, 0, 1, 2, 21, 22, 23, 12, 13, 14, 15, 16, 17, 18, 19, 20], [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]

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]]

derived = [[4, 5, 6, 7, 8, 9, 10, 11, 0, 1, 2, 3, 16, 17, 18, 19, 20, 21, 22, 23, 12, 13, 14, 15], [4, 5, 6, 7, 8, 9, 10, 11, 0, 1, 2, 3, 20, 21, 22, 23, 12, 13, 14, 15, 16, 17, 18, 19], [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]

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]]

derived = [[5, 6, 7, 8, 9, 10, 11, 0, 1, 2, 3, 4, 17, 18, 19, 20, 21, 22, 23, 12, 13, 14, 15, 16], [5, 6, 7, 8, 9, 10, 11, 0, 1, 2, 3, 4, 19, 20, 21, 22, 23, 12, 13, 14, 15, 16, 17, 18], [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]

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]]

derived = [[6, 7, 8, 9, 10, 11, 0, 1, 2, 3, 4, 5, 18, 19, 20, 21, 22, 23, 12, 13, 14, 15, 16, 17], [6, 7, 8, 9, 10, 11, 0, 1, 2, 3, 4, 5, 18, 19, 20, 21, 22, 23, 12, 13, 14, 15, 16, 17], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], 是]

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]]

derived = [[7, 8, 9, 10, 11, 0, 1, 2, 3, 4, 5, 6, 19, 20, 21, 22, 23, 12, 13, 14, 15, 16, 17, 18], [7, 8, 9, 10, 11, 0, 1, 2, 3, 4, 5, 6, 17, 18, 19, 20, 21, 22, 23, 12, 13, 14, 15, 16], [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]

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]]

derived = [[8, 9, 10, 11, 0, 1, 2, 3, 4, 5, 6, 7, 20, 21, 22, 23, 12, 13, 14, 15, 16, 17, 18, 19], [8, 9, 10, 11, 0, 1, 2, 3, 4, 5, 6, 7, 16, 17, 18, 19, 20, 21, 22, 23, 12, 13, 14, 15], [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]

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]]

derived = [[9, 10, 11, 0, 1, 2, 3, 4, 5, 6, 7, 8, 21, 22, 23, 12, 13, 14, 15, 16, 17, 18, 19, 20], [9, 10, 11, 0, 1, 2, 3, 4, 5, 6, 7, 8, 15, 16, 17, 18, 19, 20, 21, 22, 23, 12, 13, 14], [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]

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]]

derived = [[10, 11, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 22, 23, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21], [10, 11, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 12, 13], [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]

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]]

derived = [[11, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 23, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22], [11, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 12], [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]

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]]

derived = [[12, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 0, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1], [12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [是, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否], 否]

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]]

derived = [[13, 12, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 1, 0, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2], [13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 12, 11, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10], [是, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否], 否]

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]]

derived = [[14, 13, 12, 23, 22, 21, 20, 19, 18, 17, 16, 15, 2, 1, 0, 11, 10, 9, 8, 7, 6, 5, 4, 3], [14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 12, 13, 10, 11, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [是, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 是, 否, 否, 否], 否]

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]]

derived = [[15, 14, 13, 12, 23, 22, 21, 20, 19, 18, 17, 16, 3, 2, 1, 0, 11, 10, 9, 8, 7, 6, 5, 4], [15, 16, 17, 18, 19, 20, 21, 22, 23, 12, 13, 14, 9, 10, 11, 0, 1, 2, 3, 4, 5, 6, 7, 8], [是, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 是, 否, 否], 否]

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]]

derived = [[16, 15, 14, 13, 12, 23, 22, 21, 20, 19, 18, 17, 4, 3, 2, 1, 0, 11, 10, 9, 8, 7, 6, 5], [16, 17, 18, 19, 20, 21, 22, 23, 12, 13, 14, 15, 8, 9, 10, 11, 0, 1, 2, 3, 4, 5, 6, 7], [是, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 是, 否], 否]

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]]

derived = [[17, 16, 15, 14, 13, 12, 23, 22, 21, 20, 19, 18, 5, 4, 3, 2, 1, 0, 11, 10, 9, 8, 7, 6], [17, 18, 19, 20, 21, 22, 23, 12, 13, 14, 15, 16, 7, 8, 9, 10, 11, 0, 1, 2, 3, 4, 5, 6], [是, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 是], 否]

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]]

derived = [[18, 17, 16, 15, 14, 13, 12, 23, 22, 21, 20, 19, 6, 5, 4, 3, 2, 1, 0, 11, 10, 9, 8, 7], [18, 19, 20, 21, 22, 23, 12, 13, 14, 15, 16, 17, 6, 7, 8, 9, 10, 11, 0, 1, 2, 3, 4, 5], [是, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否], 否]

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]]

derived = [[19, 18, 17, 16, 15, 14, 13, 12, 23, 22, 21, 20, 7, 6, 5, 4, 3, 2, 1, 0, 11, 10, 9, 8], [19, 20, 21, 22, 23, 12, 13, 14, 15, 16, 17, 18, 5, 6, 7, 8, 9, 10, 11, 0, 1, 2, 3, 4], [是, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否], 否]

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]]

derived = [[20, 19, 18, 17, 16, 15, 14, 13, 12, 23, 22, 21, 8, 7, 6, 5, 4, 3, 2, 1, 0, 11, 10, 9], [20, 21, 22, 23, 12, 13, 14, 15, 16, 17, 18, 19, 4, 5, 6, 7, 8, 9, 10, 11, 0, 1, 2, 3], [是, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 是, 否, 否, 否], 否]

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]]

derived = [[21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 23, 22, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 11, 10], [21, 22, 23, 12, 13, 14, 15, 16, 17, 18, 19, 20, 3, 4, 5, 6, 7, 8, 9, 10, 11, 0, 1, 2], [是, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 是, 否, 否], 否]

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]]

derived = [[22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 23, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 11], [22, 23, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 0, 1], [是, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 是, 否], 否]

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]]

derived = [[23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0], [23, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 0], [是, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 是], 否]

source roles = [Center ACTUAL Z, [0, 6], 0]

derived = [是, [[0, 0, 0, 是], [0, 6, 6, 是], [6, 0, 6, 是], [6, 6, 0, 是]], 是, [[0, 0, 是], [6, 6, 是]], 是, 是, [[0, [0, 6], 是], [1, [0, 6], 是], [2, [0, 6], 是], [3, [0, 6], 是], [4, [0, 6], 是], [5, [0, 6], 是], [6, [0, 6], 是], [7, [0, 6], 是], [8, [0, 6], 是], [9, [0, 6], 是], [10, [0, 6], 是], [11, [0, 6], 是], [12, [0, 6], 是], [13, [0, 6], 是], [14, [0, 6], 是], [15, [0, 6], 是], [16, [0, 6], 是], [17, [0, 6], 是], [18, [0, 6], 是], [19, [0, 6], 是], [20, [0, 6], 是], [21, [0, 6], 是], [22, [0, 6], 是], [23, [0, 6], 是]], 是]

source roles = [[0, 6], [[是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 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], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 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, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否], [是, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否], [是, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否], [是, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 是, 否, 否, 否], [是, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 是, 否, 否], [是, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 是, 否], [是, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 是], [是, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否], [是, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否], [是, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 是, 否, 否, 否], [是, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 是, 否, 否], [是, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 是, 否], [是, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 否, 否, 否, 否, 否, 是, 否, 否, 否, 否, 否, 是]]]

derived = [是, 是, central z: g*z*g^-1=z for EVERY g]

逐步反向核對

• 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, 6], [[0, [0, 6], 是], [1, [0, 6], 是], [2, [0, 6], 是], [3, [0, 6], 是], [4, [0, 6], 是], [5, [0, 6], 是], [6, [0, 6], 是], [7, [0, 6], 是], [8, [0, 6], 是], [9, [0, 6], 是], [10, [0, 6], 是], [11, [0, 6], 是], [12, [0, 6], 是], [13, [0, 6], 是], [14, [0, 6], 是], [15, [0, 6], 是], [16, [0, 6], 是], [17, [0, 6], 是], [18, [0, 6], 是], [19, [0, 6], 是], [20, [0, 6], 是], [21, [0, 6], 是], [22, [0, 6], 是], [23, [0, 6], 是]], 是, every_conjugate_of_a_central_element_remains_the_same_central_element)

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。