# 第 24808 題：有限群共軛類 [返回所在分頁 125](https://ocme.evemisslab.com/zh-Hant/questions/page/125/) [← 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-20261114-r03-finite-group-conjugacy-class-foundations/#q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0008) 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。 R0048-24808 · q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0008 ## 原題與已知條件 由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-action-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],[1,2,3,4,5,6,7,8,9,0,11,12,13,14,15,16,17,18,19,10],[2,3,4,5,6,7,8,9,0,1,12,13,14,15,16,17,18,19,10,11],[3,4,5,6,7,8,9,0,1,2,13,14,15,16,17,18,19,10,11,12],[4,5,6,7,8,9,0,1,2,3,14,15,16,17,18,19,10,11,12,13],[5,6,7,8,9,0,1,2,3,4,15,16,17,18,19,10,11,12,13,14],[6,7,8,9,0,1,2,3,4,5,16,17,18,19,10,11,12,13,14,15],[7,8,9,0,1,2,3,4,5,6,17,18,19,10,11,12,13,14,15,16],[8,9,0,1,2,3,4,5,6,7,18,19,10,11,12,13,14,15,16,17],[9,0,1,2,3,4,5,6,7,8,19,10,11,12,13,14,15,16,17,18],[10,19,18,17,16,15,14,13,12,11,0,9,8,7,6,5,4,3,2,1],[11,10,19,18,17,16,15,14,13,12,1,0,9,8,7,6,5,4,3,2],[12,11,10,19,18,17,16,15,14,13,2,1,0,9,8,7,6,5,4,3],[13,12,11,10,19,18,17,16,15,14,3,2,1,0,9,8,7,6,5,4],[14,13,12,11,10,19,18,17,16,15,4,3,2,1,0,9,8,7,6,5],[15,14,13,12,11,10,19,18,17,16,5,4,3,2,1,0,9,8,7,6],[16,15,14,13,12,11,10,19,18,17,6,5,4,3,2,1,0,9,8,7],[17,16,15,14,13,12,11,10,19,18,7,6,5,4,3,2,1,0,9,8],[18,17,16,15,14,13,12,11,10,19,8,7,6,5,4,3,2,1,0,9],[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 — 由完整Cayley table導出全部conjugation action與orbits。操作=conjugacy-action-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],[1,2,3,4,5,6,7,8,9,0,11,12,13,14,15,16,17,18,19,10],[2,3,4,5,6,7,8,9,0,1,12,13,14,15,16,17,18,19,10,11],[3,4,5,6,7,8,9,0,1,2,13,14,15,16,17,18,19,10,11,12],[4,5,6,7,8,9,0,1,2,3,14,15,16,17,18,19,10,11,12,13],[5,6,7,8,9,0,1,2,3,4,15,16,17,18,19,10,11,12,13,14],[6,7,8,9,0,1,2,3,4,5,16,17,18,19,10,11,12,13,14,15],[7,8,9,0,1,2,3,4,5,6,17,18,19,10,11,12,13,14,15,16],[8,9,0,1,2,3,4,5,6,7,18,19,10,11,12,13,14,15,16,17],[9,0,1,2,3,4,5,6,7,8,19,10,11,12,13,14,15,16,17,18],[10,19,18,17,16,15,14,13,12,11,0,9,8,7,6,5,4,3,2,1],[11,10,19,18,17,16,15,14,13,12,1,0,9,8,7,6,5,4,3,2],[12,11,10,19,18,17,16,15,14,13,2,1,0,9,8,7,6,5,4,3],[13,12,11,10,19,18,17,16,15,14,3,2,1,0,9,8,7,6,5,4],[14,13,12,11,10,19,18,17,16,15,4,3,2,1,0,9,8,7,6,5],[15,14,13,12,11,10,19,18,17,16,5,4,3,2,1,0,9,8,7,6],[16,15,14,13,12,11,10,19,18,17,6,5,4,3,2,1,0,9,8,7],[17,16,15,14,13,12,11,10,19,18,7,6,5,4,3,2,1,0,9,8],[18,17,16,15,14,13,12,11,10,19,8,7,6,5,4,3,2,1,0,9],[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-conjugacy-class](https://ocme.evemisslab.com/zh-Hant/mko/mko-finite-group-conjugacy-class/) ## 逐步推導 S001 · implies操作前 source roles = [conjugacy-action-table] 操作後 derived = [[conjugation_action, identity_action, composition_action, certificate]] 條件：無 直接列來源完整欄序，不需JavaScript；原題、布林旗標、數學物件與非聲稱保持分層。 步驟識別與依賴規則：source_ordered_fields_without_JS · 依賴：G001 S002 · implies操作前 source roles = [Conjugacy ORIGINAL group, 64, [[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19], [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 11, 12, 13, 14, 15, 16, 17, 18, 19, 10], [2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 12, 13, 14, 15, 16, 17, 18, 19, 10, 11], [3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 13, 14, 15, 16, 17, 18, 19, 10, 11, 12], [4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 14, 15, 16, 17, 18, 19, 10, 11, 12, 13], [5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 15, 16, 17, 18, 19, 10, 11, 12, 13, 14], [6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 16, 17, 18, 19, 10, 11, 12, 13, 14, 15], [7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 17, 18, 19, 10, 11, 12, 13, 14, 15, 16], [8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 18, 19, 10, 11, 12, 13, 14, 15, 16, 17], [9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 19, 10, 11, 12, 13, 14, 15, 16, 17, 18], [10, 19, 18, 17, 16, 15, 14, 13, 12, 11, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1], [11, 10, 19, 18, 17, 16, 15, 14, 13, 12, 1, 0, 9, 8, 7, 6, 5, 4, 3, 2], [12, 11, 10, 19, 18, 17, 16, 15, 14, 13, 2, 1, 0, 9, 8, 7, 6, 5, 4, 3], [13, 12, 11, 10, 19, 18, 17, 16, 15, 14, 3, 2, 1, 0, 9, 8, 7, 6, 5, 4], [14, 13, 12, 11, 10, 19, 18, 17, 16, 15, 4, 3, 2, 1, 0, 9, 8, 7, 6, 5], [15, 14, 13, 12, 11, 10, 19, 18, 17, 16, 5, 4, 3, 2, 1, 0, 9, 8, 7, 6], [16, 15, 14, 13, 12, 11, 10, 19, 18, 17, 6, 5, 4, 3, 2, 1, 0, 9, 8, 7], [17, 16, 15, 14, 13, 12, 11, 10, 19, 18, 7, 6, 5, 4, 3, 2, 1, 0, 9, 8], [18, 17, 16, 15, 14, 13, 12, 11, 10, 19, 8, 7, 6, 5, 4, 3, 2, 1, 0, 9], [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 = [20, [[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]], 是] 條件：無 先驗完整n×n閉合表與實際identity標籤，非預設0。mod44上限32，mod45上限64；同一carrier不能混入另一表。 步驟識別與依賴規則：Group_complete_Cayley_signature_actual_identity · 依賴：G001, S001 S003 · implies操作前 source roles = [Conjugacy ORIGINAL group, 20, FOR EVERY x,y,z in0..n-1] 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]], 8000, 是] 條件：無 矩陣(x,y)逐全部z核(xy)z=x(yz)，故涵蓋全部n³三元組，不是抽樣。表已在前步完整列出，不重印數百萬同義查表項。 步驟識別與依賴規則：Group_ALL_associativity_triples_compact_complete_pair_matrix · 依賴：G001, S002 S004 · implies操作前 source roles = [Conjugacy ORIGINAL group, 0] 操作後 derived = [[0, 9, 8, 7, 6, 5, 4, 3, 2, 1, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19], [[0, 0, 0, 0], [1, 9, 0, 0], [2, 8, 0, 0], [3, 7, 0, 0], [4, 6, 0, 0], [5, 5, 0, 0], [6, 4, 0, 0], [7, 3, 0, 0], [8, 2, 0, 0], [9, 1, 0, 0], [10, 10, 0, 0], [11, 11, 0, 0], [12, 12, 0, 0], [13, 13, 0, 0], [14, 14, 0, 0], [15, 15, 0, 0], [16, 16, 0, 0], [17, 17, 0, 0], [18, 18, 0, 0], [19, 19, 0, 0]], 是] 條件：無 每個元素的左、右逆都要回到同一實際identity；結合律使兩側逆唯一。這才完成群前提。 步驟識別與依賴規則：Group_ALL_two_sided_inverses · 依賴：G001, S003 S005 · implies操作前 source roles = [0, 0, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19]] 操作後 derived = [[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19]] 條件：無 對每個原元素x先算gx再乘g^-1，形成完整acting row；這是element action，不是conjugate subgroup。 步驟識別與依賴規則：Conjugacy_EVERY_g_EVERY_element_exact_action_row · 依賴：G001, S004 S006 · implies操作前 source roles = [1, 9, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19]] 操作後 derived = [[1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 11, 12, 13, 14, 15, 16, 17, 18, 19, 10], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 13, 14, 15, 16, 17, 18, 19, 10, 11]] 條件：無 對每個原元素x先算gx再乘g^-1，形成完整acting row；這是element action，不是conjugate subgroup。 步驟識別與依賴規則：Conjugacy_EVERY_g_EVERY_element_exact_action_row · 依賴：G001, S005 S007 · implies操作前 source roles = [2, 8, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19]] 操作後 derived = [[2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 12, 13, 14, 15, 16, 17, 18, 19, 10, 11], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 14, 15, 16, 17, 18, 19, 10, 11, 12, 13]] 條件：無 對每個原元素x先算gx再乘g^-1，形成完整acting row；這是element action，不是conjugate subgroup。 步驟識別與依賴規則：Conjugacy_EVERY_g_EVERY_element_exact_action_row · 依賴：G001, S006 S008 · implies操作前 source roles = [3, 7, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19]] 操作後 derived = [[3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 13, 14, 15, 16, 17, 18, 19, 10, 11, 12], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 16, 17, 18, 19, 10, 11, 12, 13, 14, 15]] 條件：無 對每個原元素x先算gx再乘g^-1，形成完整acting row；這是element action，不是conjugate subgroup。 步驟識別與依賴規則：Conjugacy_EVERY_g_EVERY_element_exact_action_row · 依賴：G001, S007 S009 · implies操作前 source roles = [4, 6, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19]] 操作後 derived = [[4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 14, 15, 16, 17, 18, 19, 10, 11, 12, 13], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 18, 19, 10, 11, 12, 13, 14, 15, 16, 17]] 條件：無 對每個原元素x先算gx再乘g^-1，形成完整acting row；這是element action，不是conjugate subgroup。 步驟識別與依賴規則：Conjugacy_EVERY_g_EVERY_element_exact_action_row · 依賴：G001, S008 S010 · implies操作前 source roles = [5, 5, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19]] 操作後 derived = [[5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 15, 16, 17, 18, 19, 10, 11, 12, 13, 14], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19]] 條件：無 對每個原元素x先算gx再乘g^-1，形成完整acting row；這是element action，不是conjugate subgroup。 步驟識別與依賴規則：Conjugacy_EVERY_g_EVERY_element_exact_action_row · 依賴：G001, S009 S011 · implies操作前 source roles = [6, 4, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19]] 操作後 derived = [[6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 16, 17, 18, 19, 10, 11, 12, 13, 14, 15], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 13, 14, 15, 16, 17, 18, 19, 10, 11]] 條件：無 對每個原元素x先算gx再乘g^-1，形成完整acting row；這是element action，不是conjugate subgroup。 步驟識別與依賴規則：Conjugacy_EVERY_g_EVERY_element_exact_action_row · 依賴：G001, S010 S012 · implies操作前 source roles = [7, 3, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19]] 操作後 derived = [[7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 17, 18, 19, 10, 11, 12, 13, 14, 15, 16], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 14, 15, 16, 17, 18, 19, 10, 11, 12, 13]] 條件：無 對每個原元素x先算gx再乘g^-1，形成完整acting row；這是element action，不是conjugate subgroup。 步驟識別與依賴規則：Conjugacy_EVERY_g_EVERY_element_exact_action_row · 依賴：G001, S011 S013 · implies操作前 source roles = [8, 2, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19]] 操作後 derived = [[8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 18, 19, 10, 11, 12, 13, 14, 15, 16, 17], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 16, 17, 18, 19, 10, 11, 12, 13, 14, 15]] 條件：無 對每個原元素x先算gx再乘g^-1，形成完整acting row；這是element action，不是conjugate subgroup。 步驟識別與依賴規則：Conjugacy_EVERY_g_EVERY_element_exact_action_row · 依賴：G001, S012 S014 · implies操作前 source roles = [9, 1, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19]] 操作後 derived = [[9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 19, 10, 11, 12, 13, 14, 15, 16, 17, 18], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 18, 19, 10, 11, 12, 13, 14, 15, 16, 17]] 條件：無 對每個原元素x先算gx再乘g^-1，形成完整acting row；這是element action，不是conjugate subgroup。 步驟識別與依賴規則：Conjugacy_EVERY_g_EVERY_element_exact_action_row · 依賴：G001, S013 S015 · implies操作前 source roles = [10, 10, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19]] 操作後 derived = [[10, 19, 18, 17, 16, 15, 14, 13, 12, 11, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1], [0, 9, 8, 7, 6, 5, 4, 3, 2, 1, 10, 19, 18, 17, 16, 15, 14, 13, 12, 11]] 條件：無 對每個原元素x先算gx再乘g^-1，形成完整acting row；這是element action，不是conjugate subgroup。 步驟識別與依賴規則：Conjugacy_EVERY_g_EVERY_element_exact_action_row · 依賴：G001, S014 S016 · implies操作前 source roles = [11, 11, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19]] 操作後 derived = [[11, 10, 19, 18, 17, 16, 15, 14, 13, 12, 1, 0, 9, 8, 7, 6, 5, 4, 3, 2], [0, 9, 8, 7, 6, 5, 4, 3, 2, 1, 12, 11, 10, 19, 18, 17, 16, 15, 14, 13]] 條件：無 對每個原元素x先算gx再乘g^-1，形成完整acting row；這是element action，不是conjugate subgroup。 步驟識別與依賴規則：Conjugacy_EVERY_g_EVERY_element_exact_action_row · 依賴：G001, S015 S017 · implies操作前 source roles = [12, 12, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19]] 操作後 derived = [[12, 11, 10, 19, 18, 17, 16, 15, 14, 13, 2, 1, 0, 9, 8, 7, 6, 5, 4, 3], [0, 9, 8, 7, 6, 5, 4, 3, 2, 1, 14, 13, 12, 11, 10, 19, 18, 17, 16, 15]] 條件：無 對每個原元素x先算gx再乘g^-1，形成完整acting row；這是element action，不是conjugate subgroup。 步驟識別與依賴規則：Conjugacy_EVERY_g_EVERY_element_exact_action_row · 依賴：G001, S016 S018 · implies操作前 source roles = [13, 13, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19]] 操作後 derived = [[13, 12, 11, 10, 19, 18, 17, 16, 15, 14, 3, 2, 1, 0, 9, 8, 7, 6, 5, 4], [0, 9, 8, 7, 6, 5, 4, 3, 2, 1, 16, 15, 14, 13, 12, 11, 10, 19, 18, 17]] 條件：無 對每個原元素x先算gx再乘g^-1，形成完整acting row；這是element action，不是conjugate subgroup。 步驟識別與依賴規則：Conjugacy_EVERY_g_EVERY_element_exact_action_row · 依賴：G001, S017 S019 · implies操作前 source roles = [14, 14, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19]] 操作後 derived = [[14, 13, 12, 11, 10, 19, 18, 17, 16, 15, 4, 3, 2, 1, 0, 9, 8, 7, 6, 5], [0, 9, 8, 7, 6, 5, 4, 3, 2, 1, 18, 17, 16, 15, 14, 13, 12, 11, 10, 19]] 條件：無 對每個原元素x先算gx再乘g^-1，形成完整acting row；這是element action，不是conjugate subgroup。 步驟識別與依賴規則：Conjugacy_EVERY_g_EVERY_element_exact_action_row · 依賴：G001, S018 S020 · implies操作前 source roles = [15, 15, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19]] 操作後 derived = [[15, 14, 13, 12, 11, 10, 19, 18, 17, 16, 5, 4, 3, 2, 1, 0, 9, 8, 7, 6], [0, 9, 8, 7, 6, 5, 4, 3, 2, 1, 10, 19, 18, 17, 16, 15, 14, 13, 12, 11]] 條件：無 對每個原元素x先算gx再乘g^-1，形成完整acting row；這是element action，不是conjugate subgroup。 步驟識別與依賴規則：Conjugacy_EVERY_g_EVERY_element_exact_action_row · 依賴：G001, S019 S021 · implies操作前 source roles = [16, 16, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19]] 操作後 derived = [[16, 15, 14, 13, 12, 11, 10, 19, 18, 17, 6, 5, 4, 3, 2, 1, 0, 9, 8, 7], [0, 9, 8, 7, 6, 5, 4, 3, 2, 1, 12, 11, 10, 19, 18, 17, 16, 15, 14, 13]] 條件：無 對每個原元素x先算gx再乘g^-1，形成完整acting row；這是element action，不是conjugate subgroup。 步驟識別與依賴規則：Conjugacy_EVERY_g_EVERY_element_exact_action_row · 依賴：G001, S020 S022 · implies操作前 source roles = [17, 17, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19]] 操作後 derived = [[17, 16, 15, 14, 13, 12, 11, 10, 19, 18, 7, 6, 5, 4, 3, 2, 1, 0, 9, 8], [0, 9, 8, 7, 6, 5, 4, 3, 2, 1, 14, 13, 12, 11, 10, 19, 18, 17, 16, 15]] 條件：無 對每個原元素x先算gx再乘g^-1，形成完整acting row；這是element action，不是conjugate subgroup。 步驟識別與依賴規則：Conjugacy_EVERY_g_EVERY_element_exact_action_row · 依賴：G001, S021 S023 · implies操作前 source roles = [18, 18, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19]] 操作後 derived = [[18, 17, 16, 15, 14, 13, 12, 11, 10, 19, 8, 7, 6, 5, 4, 3, 2, 1, 0, 9], [0, 9, 8, 7, 6, 5, 4, 3, 2, 1, 16, 15, 14, 13, 12, 11, 10, 19, 18, 17]] 條件：無 對每個原元素x先算gx再乘g^-1，形成完整acting row；這是element action，不是conjugate subgroup。 步驟識別與依賴規則：Conjugacy_EVERY_g_EVERY_element_exact_action_row · 依賴：G001, S022 S024 · implies操作前 source roles = [19, 19, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19]] 操作後 derived = [[19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0], [0, 9, 8, 7, 6, 5, 4, 3, 2, 1, 18, 17, 16, 15, 14, 13, 12, 11, 10, 19]] 條件：無 對每個原元素x先算gx再乘g^-1，形成完整acting row；這是element action，不是conjugate subgroup。 步驟識別與依賴規則：Conjugacy_EVERY_g_EVERY_element_exact_action_row · 依賴：G001, S023 S025 · implies操作前 source roles = [0, 20, [[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 13, 14, 15, 16, 17, 18, 19, 10, 11], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 14, 15, 16, 17, 18, 19, 10, 11, 12, 13], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 16, 17, 18, 19, 10, 11, 12, 13, 14, 15], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 18, 19, 10, 11, 12, 13, 14, 15, 16, 17], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 13, 14, 15, 16, 17, 18, 19, 10, 11], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 14, 15, 16, 17, 18, 19, 10, 11, 12, 13], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 16, 17, 18, 19, 10, 11, 12, 13, 14, 15], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 18, 19, 10, 11, 12, 13, 14, 15, 16, 17], [0, 9, 8, 7, 6, 5, 4, 3, 2, 1, 10, 19, 18, 17, 16, 15, 14, 13, 12, 11], [0, 9, 8, 7, 6, 5, 4, 3, 2, 1, 12, 11, 10, 19, 18, 17, 16, 15, 14, 13], [0, 9, 8, 7, 6, 5, 4, 3, 2, 1, 14, 13, 12, 11, 10, 19, 18, 17, 16, 15], [0, 9, 8, 7, 6, 5, 4, 3, 2, 1, 16, 15, 14, 13, 12, 11, 10, 19, 18, 17], [0, 9, 8, 7, 6, 5, 4, 3, 2, 1, 18, 17, 16, 15, 14, 13, 12, 11, 10, 19], [0, 9, 8, 7, 6, 5, 4, 3, 2, 1, 10, 19, 18, 17, 16, 15, 14, 13, 12, 11], [0, 9, 8, 7, 6, 5, 4, 3, 2, 1, 12, 11, 10, 19, 18, 17, 16, 15, 14, 13], [0, 9, 8, 7, 6, 5, 4, 3, 2, 1, 14, 13, 12, 11, 10, 19, 18, 17, 16, 15], [0, 9, 8, 7, 6, 5, 4, 3, 2, 1, 16, 15, 14, 13, 12, 11, 10, 19, 18, 17], [0, 9, 8, 7, 6, 5, 4, 3, 2, 1, 18, 17, 16, 15, 14, 13, 12, 11, 10, 19]]] 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, (gh)x(gh)^-1=g(hxh^-1)g^-1] 條件：無 逐全部g,h,x核composition，亦由(gh)^-1=h^-1g^-1及結合律推同一公式；identity另驗。不是僅列出一個action表就假定axioms。 步驟識別與依賴規則：Conjugacy_ALL_action_axioms_and_GENERAL_algebra · 依賴：G001, S024 S026 · implies操作前 source roles = [[[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 13, 14, 15, 16, 17, 18, 19, 10, 11], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 14, 15, 16, 17, 18, 19, 10, 11, 12, 13], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 16, 17, 18, 19, 10, 11, 12, 13, 14, 15], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 18, 19, 10, 11, 12, 13, 14, 15, 16, 17], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 13, 14, 15, 16, 17, 18, 19, 10, 11], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 14, 15, 16, 17, 18, 19, 10, 11, 12, 13], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 16, 17, 18, 19, 10, 11, 12, 13, 14, 15], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 18, 19, 10, 11, 12, 13, 14, 15, 16, 17], [0, 9, 8, 7, 6, 5, 4, 3, 2, 1, 10, 19, 18, 17, 16, 15, 14, 13, 12, 11], [0, 9, 8, 7, 6, 5, 4, 3, 2, 1, 12, 11, 10, 19, 18, 17, 16, 15, 14, 13], [0, 9, 8, 7, 6, 5, 4, 3, 2, 1, 14, 13, 12, 11, 10, 19, 18, 17, 16, 15], [0, 9, 8, 7, 6, 5, 4, 3, 2, 1, 16, 15, 14, 13, 12, 11, 10, 19, 18, 17], [0, 9, 8, 7, 6, 5, 4, 3, 2, 1, 18, 17, 16, 15, 14, 13, 12, 11, 10, 19], [0, 9, 8, 7, 6, 5, 4, 3, 2, 1, 10, 19, 18, 17, 16, 15, 14, 13, 12, 11], [0, 9, 8, 7, 6, 5, 4, 3, 2, 1, 12, 11, 10, 19, 18, 17, 16, 15, 14, 13], [0, 9, 8, 7, 6, 5, 4, 3, 2, 1, 14, 13, 12, 11, 10, 19, 18, 17, 16, 15], [0, 9, 8, 7, 6, 5, 4, 3, 2, 1, 16, 15, 14, 13, 12, 11, 10, 19, 18, 17], [0, 9, 8, 7, 6, 5, 4, 3, 2, 1, 18, 17, 16, 15, 14, 13, 12, 11, 10, 19]]] 操作後 derived = [[[0], [1, 9], [10, 12, 14, 16, 18], [11, 13, 15, 17, 19], [2, 8], [3, 7], [4, 6], [5]], 20, 20, 是] 條件：無 e給自反、g^-1給反向、群乘積給傳遞；故所有完整orbits相等或不交並覆蓋G。按來源coset-like列表排序不代表它們是cosets；不引centralizer/class-size或類方程。 步驟識別與依賴規則：Conjugacy_complete_orbits_equal_or_disjoint_partition · 依賴：G001, S025 ## 逐步反向核對 - 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, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 13, 14, 15, 16, 17, 18, 19, 10, 11], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 14, 15, 16, 17, 18, 19, 10, 11, 12, 13], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 16, 17, 18, 19, 10, 11, 12, 13, 14, 15], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 18, 19, 10, 11, 12, 13, 14, 15, 16, 17], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 13, 14, 15, 16, 17, 18, 19, 10, 11], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 14, 15, 16, 17, 18, 19, 10, 11, 12, 13], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 16, 17, 18, 19, 10, 11, 12, 13, 14, 15], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 18, 19, 10, 11, 12, 13, 14, 15, 16, 17], [0, 9, 8, 7, 6, 5, 4, 3, 2, 1, 10, 19, 18, 17, 16, 15, 14, 13, 12, 11], [0, 9, 8, 7, 6, 5, 4, 3, 2, 1, 12, 11, 10, 19, 18, 17, 16, 15, 14, 13], [0, 9, 8, 7, 6, 5, 4, 3, 2, 1, 14, 13, 12, 11, 10, 19, 18, 17, 16, 15], [0, 9, 8, 7, 6, 5, 4, 3, 2, 1, 16, 15, 14, 13, 12, 11, 10, 19, 18, 17], [0, 9, 8, 7, 6, 5, 4, 3, 2, 1, 18, 17, 16, 15, 14, 13, 12, 11, 10, 19], [0, 9, 8, 7, 6, 5, 4, 3, 2, 1, 10, 19, 18, 17, 16, 15, 14, 13, 12, 11], [0, 9, 8, 7, 6, 5, 4, 3, 2, 1, 12, 11, 10, 19, 18, 17, 16, 15, 14, 13], [0, 9, 8, 7, 6, 5, 4, 3, 2, 1, 14, 13, 12, 11, 10, 19, 18, 17, 16, 15], [0, 9, 8, 7, 6, 5, 4, 3, 2, 1, 16, 15, 14, 13, 12, 11, 10, 19, 18, 17], [0, 9, 8, 7, 6, 5, 4, 3, 2, 1, 18, 17, 16, 15, 14, 13, 12, 11, 10, 19]], 是, 是, g_dot_x_equals_g_x_g_inverse_is_a_complete_left_action) 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: 263e5a09a7c165be23fe254404719e7ce9092317ab3b59e6b5d28cd08d96efac - candidate record SHA-256: 2228c41700fcee491c6e4a451224be8c6e783cd067d08c6f9eec54414817e47d - semantic review receipt SHA-256: 049a9e07e69fead88d93b34f0937b9470a06d71c1a8d097058fc83554529bdd0 - question-first witness SHA-256: 0c71ebb418f3de347d232d159fc25e93036f4ab9166bcfb5ee5b4be86d5c55b9 - Lean: NOT_RUN · human review: NOT_PERFORMED [同源完整 JSON](https://ocme.evemisslab.com/data/question-derivations/questions/q-20261015-advance-20261114-r03-finite-group-conjugacy-class-0008.json)