第 24545 題：有限正規子群

原題與已知條件

完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-left-right-coset-audit；資料={"group_table":[[9,10,11,0,1,2,3,4,5,6,7,8],[10,11,0,1,2,3,4,5,6,7,8,9],[11,0,1,2,3,4,5,6,7,8,9,10],[0,1,2,3,4,5,6,7,8,9,10,11],[1,2,3,4,5,6,7,8,9,10,11,0],[2,3,4,5,6,7,8,9,10,11,0,1],[3,4,5,6,7,8,9,10,11,0,1,2],[4,5,6,7,8,9,10,11,0,1,2,3],[5,6,7,8,9,10,11,0,1,2,3,4],[6,7,8,9,10,11,0,1,2,3,4,5],[7,8,9,10,11,0,1,2,3,4,5,6],[8,9,10,11,0,1,2,3,4,5,6,7]],"identity":3,"subset":[0,1,2,3,4,5,6,7,8,9,10,11]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。

• G001 — 完整Cayley table、完整subgroup資格與forall g的normality責任。操作=normal-left-right-coset-audit；資料={"group_table":[[9,10,11,0,1,2,3,4,5,6,7,8],[10,11,0,1,2,3,4,5,6,7,8,9],[11,0,1,2,3,4,5,6,7,8,9,10],[0,1,2,3,4,5,6,7,8,9,10,11],[1,2,3,4,5,6,7,8,9,10,11,0],[2,3,4,5,6,7,8,9,10,11,0,1],[3,4,5,6,7,8,9,10,11,0,1,2],[4,5,6,7,8,9,10,11,0,1,2,3],[5,6,7,8,9,10,11,0,1,2,3,4],[6,7,8,9,10,11,0,1,2,3,4,5],[7,8,9,10,11,0,1,2,3,4,5,6],[8,9,10,11,0,1,2,3,4,5,6,7]],"identity":3,"subset":[0,1,2,3,4,5,6,7,8,9,10,11]}。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-normal-subgroup

逐步推導

source roles = [normal-left-right-coset-audit]

derived = [[subgroup, coset_rows, all_left_right_equal, certificate]]

source roles = [Normality ORIGINAL group, 32, [[9, 10, 11, 0, 1, 2, 3, 4, 5, 6, 7, 8], [10, 11, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [11, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 0], [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 0, 1], [3, 4, 5, 6, 7, 8, 9, 10, 11, 0, 1, 2], [4, 5, 6, 7, 8, 9, 10, 11, 0, 1, 2, 3], [5, 6, 7, 8, 9, 10, 11, 0, 1, 2, 3, 4], [6, 7, 8, 9, 10, 11, 0, 1, 2, 3, 4, 5], [7, 8, 9, 10, 11, 0, 1, 2, 3, 4, 5, 6], [8, 9, 10, 11, 0, 1, 2, 3, 4, 5, 6, 7]], 3]

derived = [12, [[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]], 是]

source roles = [Normality ORIGINAL group, 12, FOR EVERY x,y,z in0..n-1]

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]], 1728, 是]

source roles = [Normality ORIGINAL group, 3]

derived = [[6, 5, 4, 3, 2, 1, 0, 11, 10, 9, 8, 7], [[0, 6, 3, 3], [1, 5, 3, 3], [2, 4, 3, 3], [3, 3, 3, 3], [4, 2, 3, 3], [5, 1, 3, 3], [6, 0, 3, 3], [7, 11, 3, 3], [8, 10, 3, 3], [9, 9, 3, 3], [10, 8, 3, 3], [11, 7, 3, 3]], 是]

source roles = [Normality ORIGINAL H, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 3]

derived = [是, [[0, 0, 9, 是], [0, 1, 10, 是], [0, 2, 11, 是], [0, 3, 0, 是], [0, 4, 1, 是], [0, 5, 2, 是], [0, 6, 3, 是], [0, 7, 4, 是], [0, 8, 5, 是], [0, 9, 6, 是], [0, 10, 7, 是], [0, 11, 8, 是], [1, 0, 10, 是], [1, 1, 11, 是], [1, 2, 0, 是], [1, 3, 1, 是], [1, 4, 2, 是], [1, 5, 3, 是], [1, 6, 4, 是], [1, 7, 5, 是], [1, 8, 6, 是], [1, 9, 7, 是], [1, 10, 8, 是], [1, 11, 9, 是], [2, 0, 11, 是], [2, 1, 0, 是], [2, 2, 1, 是], [2, 3, 2, 是], [2, 4, 3, 是], [2, 5, 4, 是], [2, 6, 5, 是], [2, 7, 6, 是], [2, 8, 7, 是], [2, 9, 8, 是], [2, 10, 9, 是], [2, 11, 10, 是], [3, 0, 0, 是], [3, 1, 1, 是], [3, 2, 2, 是], [3, 3, 3, 是], [3, 4, 4, 是], [3, 5, 5, 是], [3, 6, 6, 是], [3, 7, 7, 是], [3, 8, 8, 是], [3, 9, 9, 是], [3, 10, 10, 是], [3, 11, 11, 是], [4, 0, 1, 是], [4, 1, 2, 是], [4, 2, 3, 是], [4, 3, 4, 是], [4, 4, 5, 是], [4, 5, 6, 是], [4, 6, 7, 是], [4, 7, 8, 是], [4, 8, 9, 是], [4, 9, 10, 是], [4, 10, 11, 是], [4, 11, 0, 是], [5, 0, 2, 是], [5, 1, 3, 是], [5, 2, 4, 是], [5, 3, 5, 是], [5, 4, 6, 是], [5, 5, 7, 是], [5, 6, 8, 是], [5, 7, 9, 是], [5, 8, 10, 是], [5, 9, 11, 是], [5, 10, 0, 是], [5, 11, 1, 是], [6, 0, 3, 是], [6, 1, 4, 是], [6, 2, 5, 是], [6, 3, 6, 是], [6, 4, 7, 是], [6, 5, 8, 是], [6, 6, 9, 是], [6, 7, 10, 是], [6, 8, 11, 是], [6, 9, 0, 是], [6, 10, 1, 是], [6, 11, 2, 是], [7, 0, 4, 是], [7, 1, 5, 是], [7, 2, 6, 是], [7, 3, 7, 是], [7, 4, 8, 是], [7, 5, 9, 是], [7, 6, 10, 是], [7, 7, 11, 是], [7, 8, 0, 是], [7, 9, 1, 是], [7, 10, 2, 是], [7, 11, 3, 是], [8, 0, 5, 是], [8, 1, 6, 是], [8, 2, 7, 是], [8, 3, 8, 是], [8, 4, 9, 是], [8, 5, 10, 是], [8, 6, 11, 是], [8, 7, 0, 是], [8, 8, 1, 是], [8, 9, 2, 是], [8, 10, 3, 是], [8, 11, 4, 是], [9, 0, 6, 是], [9, 1, 7, 是], [9, 2, 8, 是], [9, 3, 9, 是], [9, 4, 10, 是], [9, 5, 11, 是], [9, 6, 0, 是], [9, 7, 1, 是], [9, 8, 2, 是], [9, 9, 3, 是], [9, 10, 4, 是], [9, 11, 5, 是], [10, 0, 7, 是], [10, 1, 8, 是], [10, 2, 9, 是], [10, 3, 10, 是], [10, 4, 11, 是], [10, 5, 0, 是], [10, 6, 1, 是], [10, 7, 2, 是], [10, 8, 3, 是], [10, 9, 4, 是], [10, 10, 5, 是], [10, 11, 6, 是], [11, 0, 8, 是], [11, 1, 9, 是], [11, 2, 10, 是], [11, 3, 11, 是], [11, 4, 0, 是], [11, 5, 1, 是], [11, 6, 2, 是], [11, 7, 3, 是], [11, 8, 4, 是], [11, 9, 5, 是], [11, 10, 6, 是], [11, 11, 7, 是]], 是, [[0, 6, 是], [1, 5, 是], [2, 4, 是], [3, 3, 是], [4, 2, 是], [5, 1, 是], [6, 0, 是], [7, 11, 是], [8, 10, 是], [9, 9, 是], [10, 8, 是], [11, 7, 是]], 是, 是]

source roles = [Normality ORIGINAL H, 0, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 6]

derived = [[[0, 9, 6, 0], [1, 10, 6, 1], [2, 11, 6, 2], [3, 0, 6, 3], [4, 1, 6, 4], [5, 2, 6, 5], [6, 3, 6, 6], [7, 4, 6, 7], [8, 5, 6, 8], [9, 6, 6, 9], [10, 7, 6, 10], [11, 8, 6, 11]], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是]

source roles = [Normality ORIGINAL H, 1, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 5]

derived = [[[0, 10, 5, 0], [1, 11, 5, 1], [2, 0, 5, 2], [3, 1, 5, 3], [4, 2, 5, 4], [5, 3, 5, 5], [6, 4, 5, 6], [7, 5, 5, 7], [8, 6, 5, 8], [9, 7, 5, 9], [10, 8, 5, 10], [11, 9, 5, 11]], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是]

source roles = [Normality ORIGINAL H, 2, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 4]

derived = [[[0, 11, 4, 0], [1, 0, 4, 1], [2, 1, 4, 2], [3, 2, 4, 3], [4, 3, 4, 4], [5, 4, 4, 5], [6, 5, 4, 6], [7, 6, 4, 7], [8, 7, 4, 8], [9, 8, 4, 9], [10, 9, 4, 10], [11, 10, 4, 11]], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是]

source roles = [Normality ORIGINAL H, 3, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 3]

derived = [[[0, 0, 3, 0], [1, 1, 3, 1], [2, 2, 3, 2], [3, 3, 3, 3], [4, 4, 3, 4], [5, 5, 3, 5], [6, 6, 3, 6], [7, 7, 3, 7], [8, 8, 3, 8], [9, 9, 3, 9], [10, 10, 3, 10], [11, 11, 3, 11]], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是]

source roles = [Normality ORIGINAL H, 4, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 2]

derived = [[[0, 1, 2, 0], [1, 2, 2, 1], [2, 3, 2, 2], [3, 4, 2, 3], [4, 5, 2, 4], [5, 6, 2, 5], [6, 7, 2, 6], [7, 8, 2, 7], [8, 9, 2, 8], [9, 10, 2, 9], [10, 11, 2, 10], [11, 0, 2, 11]], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是]

source roles = [Normality ORIGINAL H, 5, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 1]

derived = [[[0, 2, 1, 0], [1, 3, 1, 1], [2, 4, 1, 2], [3, 5, 1, 3], [4, 6, 1, 4], [5, 7, 1, 5], [6, 8, 1, 6], [7, 9, 1, 7], [8, 10, 1, 8], [9, 11, 1, 9], [10, 0, 1, 10], [11, 1, 1, 11]], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是]

source roles = [Normality ORIGINAL H, 6, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 0]

derived = [[[0, 3, 0, 0], [1, 4, 0, 1], [2, 5, 0, 2], [3, 6, 0, 3], [4, 7, 0, 4], [5, 8, 0, 5], [6, 9, 0, 6], [7, 10, 0, 7], [8, 11, 0, 8], [9, 0, 0, 9], [10, 1, 0, 10], [11, 2, 0, 11]], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是]

source roles = [Normality ORIGINAL H, 7, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 11]

derived = [[[0, 4, 11, 0], [1, 5, 11, 1], [2, 6, 11, 2], [3, 7, 11, 3], [4, 8, 11, 4], [5, 9, 11, 5], [6, 10, 11, 6], [7, 11, 11, 7], [8, 0, 11, 8], [9, 1, 11, 9], [10, 2, 11, 10], [11, 3, 11, 11]], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是]

source roles = [Normality ORIGINAL H, 8, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 10]

derived = [[[0, 5, 10, 0], [1, 6, 10, 1], [2, 7, 10, 2], [3, 8, 10, 3], [4, 9, 10, 4], [5, 10, 10, 5], [6, 11, 10, 6], [7, 0, 10, 7], [8, 1, 10, 8], [9, 2, 10, 9], [10, 3, 10, 10], [11, 4, 10, 11]], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是]

source roles = [Normality ORIGINAL H, 9, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 9]

derived = [[[0, 6, 9, 0], [1, 7, 9, 1], [2, 8, 9, 2], [3, 9, 9, 3], [4, 10, 9, 4], [5, 11, 9, 5], [6, 0, 9, 6], [7, 1, 9, 7], [8, 2, 9, 8], [9, 3, 9, 9], [10, 4, 9, 10], [11, 5, 9, 11]], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是]

source roles = [Normality ORIGINAL H, 10, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 8]

derived = [[[0, 7, 8, 0], [1, 8, 8, 1], [2, 9, 8, 2], [3, 10, 8, 3], [4, 11, 8, 4], [5, 0, 8, 5], [6, 1, 8, 6], [7, 2, 8, 7], [8, 3, 8, 8], [9, 4, 8, 9], [10, 5, 8, 10], [11, 6, 8, 11]], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是]

source roles = [Normality ORIGINAL H, 11, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 7]

derived = [[[0, 8, 7, 0], [1, 9, 7, 1], [2, 10, 7, 2], [3, 11, 7, 3], [4, 0, 7, 4], [5, 1, 7, 5], [6, 2, 7, 6], [7, 3, 7, 7], [8, 4, 7, 8], [9, 5, 7, 9], [10, 6, 7, 10], [11, 7, 7, 11]], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是]

source roles = [0, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]]

derived = [[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是]

source roles = [1, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]]

derived = [[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是]

source roles = [2, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]]

derived = [[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是]

source roles = [3, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]]

derived = [[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是]

source roles = [4, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]]

derived = [[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是]

source roles = [5, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]]

derived = [[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是]

source roles = [6, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]]

derived = [[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是]

source roles = [7, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]]

derived = [[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是]

source roles = [8, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]]

derived = [[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是]

source roles = [9, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]]

derived = [[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是]

source roles = [10, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]]

derived = [[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是]

source roles = [11, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]]

derived = [[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是]

source roles = [[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是, 是, 是]

derived = [gHg^-1=H iff gH=Hg for EVERY g]

逐步反向核對

• S030 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S029 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S028 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S027 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S026 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S025 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S024 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S023 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S022 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S021 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S020 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S019 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S018 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S017 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S016 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S015 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S014 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S013 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S012 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S011 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S010 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S009 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S008 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S007 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S006 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S005 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S004 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S003 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S002 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S001 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。

結論

([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [[0, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [1, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [2, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [3, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [4, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [5, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [6, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [7, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [8, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [9, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [10, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是], [11, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是]], 是, left_and_right_cosets_agree_for_every_g_exactly_when_H_is_normal)

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。