本批已通過 Schema、去重、來源快照與獨立答案重算；仍未標記為人工審定。
本題庫已有對應的中英逐步詳解。原題的 candidate 與英文 ai_candidate 狀態保留；AI 覆核、有限計算與 Lean 形式證明分開標示。
batch-20261014-advance-20261107-r01-finite-group-action-foundations · 2026-10-14 · 100 題
欄序為來源綁定的呈現補充；原始 JSONL 與數學答案不變。
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-qualification；資料={"group_table":[[0,1],[1,0]],"identity":0,"point_count":2,"action_table":[[0,1],[1,0]]}。請依 [group_order, point_count, group_valid, identity_action, compatible, rows_are_permutations, valid_action] 欄序回答。
(2, 2, 是, 是, 是, 是, 是)
Wave6根層核對=(2, 2, 是, 是, 是, 是, 是)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-qualification · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-qualification；資料={"group_table":[[0,1,2],[1,2,0],[2,0,1]],"identity":0,"point_count":3,"action_table":[[0,1,2],[1,2,0],[2,0,1]]}。請依 [group_order, point_count, group_valid, identity_action, compatible, rows_are_permutations, valid_action] 欄序回答。
(3, 3, 是, 是, 是, 是, 是)
Wave6根層核對=(3, 3, 是, 是, 是, 是, 是)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-qualification · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-qualification；資料={"group_table":[[0,1,2,3],[1,2,3,0],[2,3,0,1],[3,0,1,2]],"identity":0,"point_count":4,"action_table":[[0,1,2,3],[1,2,3,0],[2,3,0,1],[3,0,1,2]]}。請依 [group_order, point_count, group_valid, identity_action, compatible, rows_are_permutations, valid_action] 欄序回答。
(4, 4, 是, 是, 是, 是, 是)
Wave6根層核對=(4, 4, 是, 是, 是, 是, 是)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-qualification · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-qualification；資料={"group_table":[[0,1,2,3,4],[1,2,3,4,0],[2,3,4,0,1],[3,4,0,1,2],[4,0,1,2,3]],"identity":0,"point_count":5,"action_table":[[0,1,2,3,4],[1,2,3,4,0],[2,3,4,0,1],[3,4,0,1,2],[4,0,1,2,3]]}。請依 [group_order, point_count, group_valid, identity_action, compatible, rows_are_permutations, valid_action] 欄序回答。
(5, 5, 是, 是, 是, 是, 是)
Wave6根層核對=(5, 5, 是, 是, 是, 是, 是)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-qualification · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-qualification；資料={"group_table":[[0,1,2,3,4,5],[1,2,3,4,5,0],[2,3,4,5,0,1],[3,4,5,0,1,2],[4,5,0,1,2,3],[5,0,1,2,3,4]],"identity":0,"point_count":6,"action_table":[[0,1,2,3,4,5],[1,2,3,4,5,0],[2,3,4,5,0,1],[3,4,5,0,1,2],[4,5,0,1,2,3],[5,0,1,2,3,4]]}。請依 [group_order, point_count, group_valid, identity_action, compatible, rows_are_permutations, valid_action] 欄序回答。
(6, 6, 是, 是, 是, 是, 是)
Wave6根層核對=(6, 6, 是, 是, 是, 是, 是)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-qualification · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-qualification；資料={"group_table":[[0,1],[1,0]],"identity":0,"point_count":3,"action_table":[[0,1,2],[1,0,2]]}。請依 [group_order, point_count, group_valid, identity_action, compatible, rows_are_permutations, valid_action] 欄序回答。
(2, 3, 是, 是, 是, 是, 是)
Wave6根層核對=(2, 3, 是, 是, 是, 是, 是)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-qualification · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-qualification；資料={"group_table":[[0,1,2],[1,2,0],[2,0,1]],"identity":0,"point_count":4,"action_table":[[0,1,2,3],[1,2,0,3],[2,0,1,3]]}。請依 [group_order, point_count, group_valid, identity_action, compatible, rows_are_permutations, valid_action] 欄序回答。
(3, 4, 是, 是, 是, 是, 是)
Wave6根層核對=(3, 4, 是, 是, 是, 是, 是)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-qualification · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-qualification；資料={"group_table":[[0,1,2,3],[1,2,3,0],[2,3,0,1],[3,0,1,2]],"identity":0,"point_count":5,"action_table":[[0,1,2,3,4],[1,2,3,0,4],[2,3,0,1,4],[3,0,1,2,4]]}。請依 [group_order, point_count, group_valid, identity_action, compatible, rows_are_permutations, valid_action] 欄序回答。
(4, 5, 是, 是, 是, 是, 是)
Wave6根層核對=(4, 5, 是, 是, 是, 是, 是)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-qualification · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-qualification；資料={"group_table":[[0,1,2,3,4],[1,2,3,4,0],[2,3,4,0,1],[3,4,0,1,2],[4,0,1,2,3]],"identity":0,"point_count":6,"action_table":[[0,1,2,3,4,5],[1,2,3,4,0,5],[2,3,4,0,1,5],[3,4,0,1,2,5],[4,0,1,2,3,5]]}。請依 [group_order, point_count, group_valid, identity_action, compatible, rows_are_permutations, valid_action] 欄序回答。
(5, 6, 是, 是, 是, 是, 是)
Wave6根層核對=(5, 6, 是, 是, 是, 是, 是)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-qualification · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-qualification；資料={"group_table":[[0,1,2,3,4,5],[1,2,3,4,5,0],[2,3,4,5,0,1],[3,4,5,0,1,2],[4,5,0,1,2,3],[5,0,1,2,3,4]],"identity":0,"point_count":7,"action_table":[[0,1,2,3,4,5,6],[1,2,3,4,5,0,6],[2,3,4,5,0,1,6],[3,4,5,0,1,2,6],[4,5,0,1,2,3,6],[5,0,1,2,3,4,6]]}。請依 [group_order, point_count, group_valid, identity_action, compatible, rows_are_permutations, valid_action] 欄序回答。
(6, 7, 是, 是, 是, 是, 是)
Wave6根層核對=(6, 7, 是, 是, 是, 是, 是)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-qualification · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-qualification；資料={"group_table":[[0,1],[1,0]],"identity":0,"point_count":4,"action_table":[[0,1,2,3],[1,0,2,3]]}。請依 [group_order, point_count, group_valid, identity_action, compatible, rows_are_permutations, valid_action] 欄序回答。
(2, 4, 是, 是, 是, 是, 是)
Wave6根層核對=(2, 4, 是, 是, 是, 是, 是)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-qualification · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-qualification；資料={"group_table":[[0,1,2],[1,2,0],[2,0,1]],"identity":0,"point_count":5,"action_table":[[0,1,2,3,4],[1,2,0,3,4],[2,0,1,3,4]]}。請依 [group_order, point_count, group_valid, identity_action, compatible, rows_are_permutations, valid_action] 欄序回答。
(3, 5, 是, 是, 是, 是, 是)
Wave6根層核對=(3, 5, 是, 是, 是, 是, 是)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-qualification · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-qualification；資料={"group_table":[[0,1,2,3],[1,2,3,0],[2,3,0,1],[3,0,1,2]],"identity":0,"point_count":6,"action_table":[[0,1,2,3,4,5],[1,2,3,0,4,5],[2,3,0,1,4,5],[3,0,1,2,4,5]]}。請依 [group_order, point_count, group_valid, identity_action, compatible, rows_are_permutations, valid_action] 欄序回答。
(4, 6, 是, 是, 是, 是, 是)
Wave6根層核對=(4, 6, 是, 是, 是, 是, 是)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-qualification · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-qualification；資料={"group_table":[[0,1,2,3,4],[1,2,3,4,0],[2,3,4,0,1],[3,4,0,1,2],[4,0,1,2,3]],"identity":0,"point_count":7,"action_table":[[0,1,2,3,4,5,6],[1,2,3,4,0,5,6],[2,3,4,0,1,5,6],[3,4,0,1,2,5,6],[4,0,1,2,3,5,6]]}。請依 [group_order, point_count, group_valid, identity_action, compatible, rows_are_permutations, valid_action] 欄序回答。
(5, 7, 是, 是, 是, 是, 是)
Wave6根層核對=(5, 7, 是, 是, 是, 是, 是)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-qualification · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-qualification；資料={"group_table":[[0,1,2,3,4,5],[1,2,3,4,5,0],[2,3,4,5,0,1],[3,4,5,0,1,2],[4,5,0,1,2,3],[5,0,1,2,3,4]],"identity":0,"point_count":8,"action_table":[[0,1,2,3,4,5,6,7],[1,2,3,4,5,0,6,7],[2,3,4,5,0,1,6,7],[3,4,5,0,1,2,6,7],[4,5,0,1,2,3,6,7],[5,0,1,2,3,4,6,7]]}。請依 [group_order, point_count, group_valid, identity_action, compatible, rows_are_permutations, valid_action] 欄序回答。
(6, 8, 是, 是, 是, 是, 是)
Wave6根層核對=(6, 8, 是, 是, 是, 是, 是)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-qualification · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-qualification；資料={"group_table":[[0,1],[1,0]],"identity":0,"point_count":5,"action_table":[[0,1,2,3,4],[1,0,2,3,4]]}。請依 [group_order, point_count, group_valid, identity_action, compatible, rows_are_permutations, valid_action] 欄序回答。
(2, 5, 是, 是, 是, 是, 是)
Wave6根層核對=(2, 5, 是, 是, 是, 是, 是)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-qualification · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-qualification；資料={"group_table":[[0,1,2],[1,2,0],[2,0,1]],"identity":0,"point_count":6,"action_table":[[0,1,2,3,4,5],[1,2,0,3,4,5],[2,0,1,3,4,5]]}。請依 [group_order, point_count, group_valid, identity_action, compatible, rows_are_permutations, valid_action] 欄序回答。
(3, 6, 是, 是, 是, 是, 是)
Wave6根層核對=(3, 6, 是, 是, 是, 是, 是)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-qualification · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-qualification；資料={"group_table":[[0,1,2,3],[1,2,3,0],[2,3,0,1],[3,0,1,2]],"identity":0,"point_count":7,"action_table":[[0,1,2,3,4,5,6],[1,2,3,0,4,5,6],[2,3,0,1,4,5,6],[3,0,1,2,4,5,6]]}。請依 [group_order, point_count, group_valid, identity_action, compatible, rows_are_permutations, valid_action] 欄序回答。
(4, 7, 是, 是, 是, 是, 是)
Wave6根層核對=(4, 7, 是, 是, 是, 是, 是)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-qualification · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-qualification；資料={"group_table":[[0,1,2,3,4],[1,2,3,4,0],[2,3,4,0,1],[3,4,0,1,2],[4,0,1,2,3]],"identity":0,"point_count":8,"action_table":[[0,1,2,3,4,5,6,7],[1,2,3,4,0,5,6,7],[2,3,4,0,1,5,6,7],[3,4,0,1,2,5,6,7],[4,0,1,2,3,5,6,7]]}。請依 [group_order, point_count, group_valid, identity_action, compatible, rows_are_permutations, valid_action] 欄序回答。
(5, 8, 是, 是, 是, 是, 是)
Wave6根層核對=(5, 8, 是, 是, 是, 是, 是)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-qualification · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-qualification；資料={"group_table":[[0,1,2,3,4,5],[1,2,3,4,5,0],[2,3,4,5,0,1],[3,4,5,0,1,2],[4,5,0,1,2,3],[5,0,1,2,3,4]],"identity":0,"point_count":9,"action_table":[[0,1,2,3,4,5,6,7,8],[1,2,3,4,5,0,6,7,8],[2,3,4,5,0,1,6,7,8],[3,4,5,0,1,2,6,7,8],[4,5,0,1,2,3,6,7,8],[5,0,1,2,3,4,6,7,8]]}。請依 [group_order, point_count, group_valid, identity_action, compatible, rows_are_permutations, valid_action] 欄序回答。
(6, 9, 是, 是, 是, 是, 是)
Wave6根層核對=(6, 9, 是, 是, 是, 是, 是)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-qualification · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-qualification；資料={"group_table":[[0,1],[1,0]],"identity":0,"point_count":6,"action_table":[[0,1,2,3,4,5],[1,0,2,3,4,5]]}。請依 [group_order, point_count, group_valid, identity_action, compatible, rows_are_permutations, valid_action] 欄序回答。
(2, 6, 是, 是, 是, 是, 是)
Wave6根層核對=(2, 6, 是, 是, 是, 是, 是)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-qualification · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-qualification；資料={"group_table":[[0,1,2],[1,2,0],[2,0,1]],"identity":0,"point_count":7,"action_table":[[0,1,2,3,4,5,6],[1,2,0,3,4,5,6],[2,0,1,3,4,5,6]]}。請依 [group_order, point_count, group_valid, identity_action, compatible, rows_are_permutations, valid_action] 欄序回答。
(3, 7, 是, 是, 是, 是, 是)
Wave6根層核對=(3, 7, 是, 是, 是, 是, 是)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-qualification · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-qualification；資料={"group_table":[[0,1,2,3],[1,2,3,0],[2,3,0,1],[3,0,1,2]],"identity":0,"point_count":8,"action_table":[[0,1,2,3,4,5,6,7],[1,2,3,0,4,5,6,7],[2,3,0,1,4,5,6,7],[3,0,1,2,4,5,6,7]]}。請依 [group_order, point_count, group_valid, identity_action, compatible, rows_are_permutations, valid_action] 欄序回答。
(4, 8, 是, 是, 是, 是, 是)
Wave6根層核對=(4, 8, 是, 是, 是, 是, 是)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-qualification · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-qualification；資料={"group_table":[[0,1,2,3,4],[1,2,3,4,0],[2,3,4,0,1],[3,4,0,1,2],[4,0,1,2,3]],"identity":0,"point_count":9,"action_table":[[0,1,2,3,4,5,6,7,8],[1,2,3,4,0,5,6,7,8],[2,3,4,0,1,5,6,7,8],[3,4,0,1,2,5,6,7,8],[4,0,1,2,3,5,6,7,8]]}。請依 [group_order, point_count, group_valid, identity_action, compatible, rows_are_permutations, valid_action] 欄序回答。
(5, 9, 是, 是, 是, 是, 是)
Wave6根層核對=(5, 9, 是, 是, 是, 是, 是)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-qualification · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-qualification；資料={"group_table":[[0,1,2,3,4,5],[1,2,3,4,5,0],[2,3,4,5,0,1],[3,4,5,0,1,2],[4,5,0,1,2,3],[5,0,1,2,3,4]],"identity":0,"point_count":10,"action_table":[[0,1,2,3,4,5,6,7,8,9],[1,2,3,4,5,0,6,7,8,9],[2,3,4,5,0,1,6,7,8,9],[3,4,5,0,1,2,6,7,8,9],[4,5,0,1,2,3,6,7,8,9],[5,0,1,2,3,4,6,7,8,9]]}。請依 [group_order, point_count, group_valid, identity_action, compatible, rows_are_permutations, valid_action] 欄序回答。
(6, 10, 是, 是, 是, 是, 是)
Wave6根層核對=(6, 10, 是, 是, 是, 是, 是)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-qualification · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-identity-audit；資料={"group_table":[[0,1],[1,0]],"identity":0,"point_count":2,"action_table":[[0,1],[1,0]]}。請依 [declared_identity, point_checks, identity_action] 欄序回答。
(0, [[0, 0, 是], [1, 1, 是]], 是)
Wave6根層核對=(0, [[0, 0, 是], [1, 1, 是]], 是)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-identity-audit · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-identity-audit；資料={"group_table":[[0,1,2],[1,2,0],[2,0,1]],"identity":0,"point_count":3,"action_table":[[0,1,2],[1,2,0],[2,0,1]]}。請依 [declared_identity, point_checks, identity_action] 欄序回答。
(0, [[0, 0, 是], [1, 1, 是], [2, 2, 是]], 是)
Wave6根層核對=(0, [[0, 0, 是], [1, 1, 是], [2, 2, 是]], 是)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-identity-audit · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-identity-audit；資料={"group_table":[[0,1,2,3],[1,2,3,0],[2,3,0,1],[3,0,1,2]],"identity":0,"point_count":4,"action_table":[[0,1,2,3],[1,2,3,0],[2,3,0,1],[3,0,1,2]]}。請依 [declared_identity, point_checks, identity_action] 欄序回答。
(0, [[0, 0, 是], [1, 1, 是], [2, 2, 是], [3, 3, 是]], 是)
Wave6根層核對=(0, [[0, 0, 是], [1, 1, 是], [2, 2, 是], [3, 3, 是]], 是)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-identity-audit · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-identity-audit；資料={"group_table":[[0,1,2,3,4],[1,2,3,4,0],[2,3,4,0,1],[3,4,0,1,2],[4,0,1,2,3]],"identity":0,"point_count":5,"action_table":[[0,1,2,3,4],[1,2,3,4,0],[2,3,4,0,1],[3,4,0,1,2],[4,0,1,2,3]]}。請依 [declared_identity, point_checks, identity_action] 欄序回答。
(0, [[0, 0, 是], [1, 1, 是], [2, 2, 是], [3, 3, 是], [4, 4, 是]], 是)
Wave6根層核對=(0, [[0, 0, 是], [1, 1, 是], [2, 2, 是], [3, 3, 是], [4, 4, 是]], 是)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-identity-audit · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-identity-audit；資料={"group_table":[[0,1,2,3,4,5],[1,2,3,4,5,0],[2,3,4,5,0,1],[3,4,5,0,1,2],[4,5,0,1,2,3],[5,0,1,2,3,4]],"identity":0,"point_count":6,"action_table":[[0,1,2,3,4,5],[1,2,3,4,5,0],[2,3,4,5,0,1],[3,4,5,0,1,2],[4,5,0,1,2,3],[5,0,1,2,3,4]]}。請依 [declared_identity, point_checks, identity_action] 欄序回答。
(0, [[0, 0, 是], [1, 1, 是], [2, 2, 是], [3, 3, 是], [4, 4, 是], [5, 5, 是]], 是)
Wave6根層核對=(0, [[0, 0, 是], [1, 1, 是], [2, 2, 是], [3, 3, 是], [4, 4, 是], [5, 5, 是]], 是)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-identity-audit · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-identity-audit；資料={"group_table":[[0,1],[1,0]],"identity":0,"point_count":3,"action_table":[[0,1,2],[1,0,2]]}。請依 [declared_identity, point_checks, identity_action] 欄序回答。
(0, [[0, 0, 是], [1, 1, 是], [2, 2, 是]], 是)
Wave6根層核對=(0, [[0, 0, 是], [1, 1, 是], [2, 2, 是]], 是)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-identity-audit · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-identity-audit；資料={"group_table":[[0,1,2],[1,2,0],[2,0,1]],"identity":0,"point_count":4,"action_table":[[0,1,2,3],[1,2,0,3],[2,0,1,3]]}。請依 [declared_identity, point_checks, identity_action] 欄序回答。
(0, [[0, 0, 是], [1, 1, 是], [2, 2, 是], [3, 3, 是]], 是)
Wave6根層核對=(0, [[0, 0, 是], [1, 1, 是], [2, 2, 是], [3, 3, 是]], 是)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-identity-audit · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-identity-audit；資料={"group_table":[[0,1,2,3],[1,2,3,0],[2,3,0,1],[3,0,1,2]],"identity":0,"point_count":5,"action_table":[[0,1,2,3,4],[1,2,3,0,4],[2,3,0,1,4],[3,0,1,2,4]]}。請依 [declared_identity, point_checks, identity_action] 欄序回答。
(0, [[0, 0, 是], [1, 1, 是], [2, 2, 是], [3, 3, 是], [4, 4, 是]], 是)
Wave6根層核對=(0, [[0, 0, 是], [1, 1, 是], [2, 2, 是], [3, 3, 是], [4, 4, 是]], 是)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-identity-audit · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-identity-audit；資料={"group_table":[[0,1,2,3,4],[1,2,3,4,0],[2,3,4,0,1],[3,4,0,1,2],[4,0,1,2,3]],"identity":0,"point_count":6,"action_table":[[0,1,2,3,4,5],[1,2,3,4,0,5],[2,3,4,0,1,5],[3,4,0,1,2,5],[4,0,1,2,3,5]]}。請依 [declared_identity, point_checks, identity_action] 欄序回答。
(0, [[0, 0, 是], [1, 1, 是], [2, 2, 是], [3, 3, 是], [4, 4, 是], [5, 5, 是]], 是)
Wave6根層核對=(0, [[0, 0, 是], [1, 1, 是], [2, 2, 是], [3, 3, 是], [4, 4, 是], [5, 5, 是]], 是)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-identity-audit · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-identity-audit；資料={"group_table":[[0,1,2,3,4,5],[1,2,3,4,5,0],[2,3,4,5,0,1],[3,4,5,0,1,2],[4,5,0,1,2,3],[5,0,1,2,3,4]],"identity":0,"point_count":7,"action_table":[[0,1,2,3,4,5,6],[1,2,3,4,5,0,6],[2,3,4,5,0,1,6],[3,4,5,0,1,2,6],[4,5,0,1,2,3,6],[5,0,1,2,3,4,6]]}。請依 [declared_identity, point_checks, identity_action] 欄序回答。
(0, [[0, 0, 是], [1, 1, 是], [2, 2, 是], [3, 3, 是], [4, 4, 是], [5, 5, 是], [6, 6, 是]], 是)
Wave6根層核對=(0, [[0, 0, 是], [1, 1, 是], [2, 2, 是], [3, 3, 是], [4, 4, 是], [5, 5, 是], [6, 6, 是]], 是)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-identity-audit · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-identity-audit；資料={"group_table":[[0,1],[1,0]],"identity":0,"point_count":4,"action_table":[[0,1,2,3],[1,0,2,3]]}。請依 [declared_identity, point_checks, identity_action] 欄序回答。
(0, [[0, 0, 是], [1, 1, 是], [2, 2, 是], [3, 3, 是]], 是)
Wave6根層核對=(0, [[0, 0, 是], [1, 1, 是], [2, 2, 是], [3, 3, 是]], 是)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-identity-audit · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-identity-audit；資料={"group_table":[[0,1,2],[1,2,0],[2,0,1]],"identity":0,"point_count":5,"action_table":[[0,1,2,3,4],[1,2,0,3,4],[2,0,1,3,4]]}。請依 [declared_identity, point_checks, identity_action] 欄序回答。
(0, [[0, 0, 是], [1, 1, 是], [2, 2, 是], [3, 3, 是], [4, 4, 是]], 是)
Wave6根層核對=(0, [[0, 0, 是], [1, 1, 是], [2, 2, 是], [3, 3, 是], [4, 4, 是]], 是)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-identity-audit · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-identity-audit；資料={"group_table":[[0,1,2,3],[1,2,3,0],[2,3,0,1],[3,0,1,2]],"identity":0,"point_count":6,"action_table":[[0,1,2,3,4,5],[1,2,3,0,4,5],[2,3,0,1,4,5],[3,0,1,2,4,5]]}。請依 [declared_identity, point_checks, identity_action] 欄序回答。
(0, [[0, 0, 是], [1, 1, 是], [2, 2, 是], [3, 3, 是], [4, 4, 是], [5, 5, 是]], 是)
Wave6根層核對=(0, [[0, 0, 是], [1, 1, 是], [2, 2, 是], [3, 3, 是], [4, 4, 是], [5, 5, 是]], 是)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-identity-audit · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-identity-audit；資料={"group_table":[[0,1,2,3,4],[1,2,3,4,0],[2,3,4,0,1],[3,4,0,1,2],[4,0,1,2,3]],"identity":0,"point_count":7,"action_table":[[0,1,2,3,4,5,6],[1,2,3,4,0,5,6],[2,3,4,0,1,5,6],[3,4,0,1,2,5,6],[4,0,1,2,3,5,6]]}。請依 [declared_identity, point_checks, identity_action] 欄序回答。
(0, [[0, 0, 是], [1, 1, 是], [2, 2, 是], [3, 3, 是], [4, 4, 是], [5, 5, 是], [6, 6, 是]], 是)
Wave6根層核對=(0, [[0, 0, 是], [1, 1, 是], [2, 2, 是], [3, 3, 是], [4, 4, 是], [5, 5, 是], [6, 6, 是]], 是)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-identity-audit · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-identity-audit；資料={"group_table":[[0,1,2,3,4,5],[1,2,3,4,5,0],[2,3,4,5,0,1],[3,4,5,0,1,2],[4,5,0,1,2,3],[5,0,1,2,3,4]],"identity":0,"point_count":8,"action_table":[[0,1,2,3,4,5,6,7],[1,2,3,4,5,0,6,7],[2,3,4,5,0,1,6,7],[3,4,5,0,1,2,6,7],[4,5,0,1,2,3,6,7],[5,0,1,2,3,4,6,7]]}。請依 [declared_identity, point_checks, identity_action] 欄序回答。
(0, [[0, 0, 是], [1, 1, 是], [2, 2, 是], [3, 3, 是], [4, 4, 是], [5, 5, 是], [6, 6, 是], [7, 7, 是]], 是)
Wave6根層核對=(0, [[0, 0, 是], [1, 1, 是], [2, 2, 是], [3, 3, 是], [4, 4, 是], [5, 5, 是], [6, 6, 是], [7, 7, 是]], 是)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-identity-audit · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-identity-audit；資料={"group_table":[[0,1],[1,0]],"identity":0,"point_count":5,"action_table":[[0,1,2,3,4],[1,0,2,3,4]]}。請依 [declared_identity, point_checks, identity_action] 欄序回答。
(0, [[0, 0, 是], [1, 1, 是], [2, 2, 是], [3, 3, 是], [4, 4, 是]], 是)
Wave6根層核對=(0, [[0, 0, 是], [1, 1, 是], [2, 2, 是], [3, 3, 是], [4, 4, 是]], 是)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-identity-audit · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-identity-audit；資料={"group_table":[[0,1,2],[1,2,0],[2,0,1]],"identity":0,"point_count":6,"action_table":[[0,1,2,3,4,5],[1,2,0,3,4,5],[2,0,1,3,4,5]]}。請依 [declared_identity, point_checks, identity_action] 欄序回答。
(0, [[0, 0, 是], [1, 1, 是], [2, 2, 是], [3, 3, 是], [4, 4, 是], [5, 5, 是]], 是)
Wave6根層核對=(0, [[0, 0, 是], [1, 1, 是], [2, 2, 是], [3, 3, 是], [4, 4, 是], [5, 5, 是]], 是)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-identity-audit · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-identity-audit；資料={"group_table":[[0,1,2,3],[1,2,3,0],[2,3,0,1],[3,0,1,2]],"identity":0,"point_count":7,"action_table":[[0,1,2,3,4,5,6],[1,2,3,0,4,5,6],[2,3,0,1,4,5,6],[3,0,1,2,4,5,6]]}。請依 [declared_identity, point_checks, identity_action] 欄序回答。
(0, [[0, 0, 是], [1, 1, 是], [2, 2, 是], [3, 3, 是], [4, 4, 是], [5, 5, 是], [6, 6, 是]], 是)
Wave6根層核對=(0, [[0, 0, 是], [1, 1, 是], [2, 2, 是], [3, 3, 是], [4, 4, 是], [5, 5, 是], [6, 6, 是]], 是)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-identity-audit · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-identity-audit；資料={"group_table":[[0,1,2,3,4],[1,2,3,4,0],[2,3,4,0,1],[3,4,0,1,2],[4,0,1,2,3]],"identity":0,"point_count":8,"action_table":[[0,1,2,3,4,5,6,7],[1,2,3,4,0,5,6,7],[2,3,4,0,1,5,6,7],[3,4,0,1,2,5,6,7],[4,0,1,2,3,5,6,7]]}。請依 [declared_identity, point_checks, identity_action] 欄序回答。
(0, [[0, 0, 是], [1, 1, 是], [2, 2, 是], [3, 3, 是], [4, 4, 是], [5, 5, 是], [6, 6, 是], [7, 7, 是]], 是)
Wave6根層核對=(0, [[0, 0, 是], [1, 1, 是], [2, 2, 是], [3, 3, 是], [4, 4, 是], [5, 5, 是], [6, 6, 是], [7, 7, 是]], 是)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-identity-audit · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-identity-audit；資料={"group_table":[[0,1,2,3,4,5],[1,2,3,4,5,0],[2,3,4,5,0,1],[3,4,5,0,1,2],[4,5,0,1,2,3],[5,0,1,2,3,4]],"identity":0,"point_count":9,"action_table":[[0,1,2,3,4,5,6,7,8],[1,2,3,4,5,0,6,7,8],[2,3,4,5,0,1,6,7,8],[3,4,5,0,1,2,6,7,8],[4,5,0,1,2,3,6,7,8],[5,0,1,2,3,4,6,7,8]]}。請依 [declared_identity, point_checks, identity_action] 欄序回答。
(0, [[0, 0, 是], [1, 1, 是], [2, 2, 是], [3, 3, 是], [4, 4, 是], [5, 5, 是], [6, 6, 是], [7, 7, 是], [8, 8, 是]], 是)
Wave6根層核對=(0, [[0, 0, 是], [1, 1, 是], [2, 2, 是], [3, 3, 是], [4, 4, 是], [5, 5, 是], [6, 6, 是], [7, 7, 是], [8, 8, 是]], 是)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-identity-audit · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-identity-audit；資料={"group_table":[[0,1],[1,0]],"identity":0,"point_count":6,"action_table":[[0,1,2,3,4,5],[1,0,2,3,4,5]]}。請依 [declared_identity, point_checks, identity_action] 欄序回答。
(0, [[0, 0, 是], [1, 1, 是], [2, 2, 是], [3, 3, 是], [4, 4, 是], [5, 5, 是]], 是)
Wave6根層核對=(0, [[0, 0, 是], [1, 1, 是], [2, 2, 是], [3, 3, 是], [4, 4, 是], [5, 5, 是]], 是)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-identity-audit · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-identity-audit；資料={"group_table":[[0,1,2],[1,2,0],[2,0,1]],"identity":0,"point_count":7,"action_table":[[0,1,2,3,4,5,6],[1,2,0,3,4,5,6],[2,0,1,3,4,5,6]]}。請依 [declared_identity, point_checks, identity_action] 欄序回答。
(0, [[0, 0, 是], [1, 1, 是], [2, 2, 是], [3, 3, 是], [4, 4, 是], [5, 5, 是], [6, 6, 是]], 是)
Wave6根層核對=(0, [[0, 0, 是], [1, 1, 是], [2, 2, 是], [3, 3, 是], [4, 4, 是], [5, 5, 是], [6, 6, 是]], 是)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-identity-audit · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-identity-audit；資料={"group_table":[[0,1,2,3],[1,2,3,0],[2,3,0,1],[3,0,1,2]],"identity":0,"point_count":8,"action_table":[[0,1,2,3,4,5,6,7],[1,2,3,0,4,5,6,7],[2,3,0,1,4,5,6,7],[3,0,1,2,4,5,6,7]]}。請依 [declared_identity, point_checks, identity_action] 欄序回答。
(0, [[0, 0, 是], [1, 1, 是], [2, 2, 是], [3, 3, 是], [4, 4, 是], [5, 5, 是], [6, 6, 是], [7, 7, 是]], 是)
Wave6根層核對=(0, [[0, 0, 是], [1, 1, 是], [2, 2, 是], [3, 3, 是], [4, 4, 是], [5, 5, 是], [6, 6, 是], [7, 7, 是]], 是)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-identity-audit · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-identity-audit；資料={"group_table":[[0,1,2,3,4],[1,2,3,4,0],[2,3,4,0,1],[3,4,0,1,2],[4,0,1,2,3]],"identity":0,"point_count":9,"action_table":[[0,1,2,3,4,5,6,7,8],[1,2,3,4,0,5,6,7,8],[2,3,4,0,1,5,6,7,8],[3,4,0,1,2,5,6,7,8],[4,0,1,2,3,5,6,7,8]]}。請依 [declared_identity, point_checks, identity_action] 欄序回答。
(0, [[0, 0, 是], [1, 1, 是], [2, 2, 是], [3, 3, 是], [4, 4, 是], [5, 5, 是], [6, 6, 是], [7, 7, 是], [8, 8, 是]], 是)
Wave6根層核對=(0, [[0, 0, 是], [1, 1, 是], [2, 2, 是], [3, 3, 是], [4, 4, 是], [5, 5, 是], [6, 6, 是], [7, 7, 是], [8, 8, 是]], 是)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-identity-audit · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-identity-audit；資料={"group_table":[[0,1,2,3,4,5],[1,2,3,4,5,0],[2,3,4,5,0,1],[3,4,5,0,1,2],[4,5,0,1,2,3],[5,0,1,2,3,4]],"identity":0,"point_count":10,"action_table":[[0,1,2,3,4,5,6,7,8,9],[1,2,3,4,5,0,6,7,8,9],[2,3,4,5,0,1,6,7,8,9],[3,4,5,0,1,2,6,7,8,9],[4,5,0,1,2,3,6,7,8,9],[5,0,1,2,3,4,6,7,8,9]]}。請依 [declared_identity, point_checks, identity_action] 欄序回答。
(0, [[0, 0, 是], [1, 1, 是], [2, 2, 是], [3, 3, 是], [4, 4, 是], [5, 5, 是], [6, 6, 是], [7, 7, 是], [8, 8, 是], [9, 9, 是]], 是)
Wave6根層核對=(0, [[0, 0, 是], [1, 1, 是], [2, 2, 是], [3, 3, 是], [4, 4, 是], [5, 5, 是], [6, 6, 是], [7, 7, 是], [8, 8, 是], [9, 9, 是]], 是)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-identity-audit · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-compatibility-audit；資料={"group_table":[[0,1],[1,0]],"identity":0,"point_count":2,"action_table":[[0,1],[1,0]]}。請依 [triple_count, first_failure, compatible, certificate] 欄序回答。
(8, null, 是, all_g_h_x_checked)
Wave6根層核對=(8, null, 是, all_g_h_x_checked)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-compatibility-audit · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-compatibility-audit；資料={"group_table":[[0,1,2],[1,2,0],[2,0,1]],"identity":0,"point_count":3,"action_table":[[0,1,2],[1,2,0],[2,0,1]]}。請依 [triple_count, first_failure, compatible, certificate] 欄序回答。
(27, null, 是, all_g_h_x_checked)
Wave6根層核對=(27, null, 是, all_g_h_x_checked)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-compatibility-audit · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-compatibility-audit；資料={"group_table":[[0,1,2,3],[1,2,3,0],[2,3,0,1],[3,0,1,2]],"identity":0,"point_count":4,"action_table":[[0,1,2,3],[1,2,3,0],[2,3,0,1],[3,0,1,2]]}。請依 [triple_count, first_failure, compatible, certificate] 欄序回答。
(64, null, 是, all_g_h_x_checked)
Wave6根層核對=(64, null, 是, all_g_h_x_checked)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-compatibility-audit · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-compatibility-audit；資料={"group_table":[[0,1,2,3,4],[1,2,3,4,0],[2,3,4,0,1],[3,4,0,1,2],[4,0,1,2,3]],"identity":0,"point_count":5,"action_table":[[0,1,2,3,4],[1,2,3,4,0],[2,3,4,0,1],[3,4,0,1,2],[4,0,1,2,3]]}。請依 [triple_count, first_failure, compatible, certificate] 欄序回答。
(125, null, 是, all_g_h_x_checked)
Wave6根層核對=(125, null, 是, all_g_h_x_checked)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-compatibility-audit · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-compatibility-audit；資料={"group_table":[[0,1,2,3,4,5],[1,2,3,4,5,0],[2,3,4,5,0,1],[3,4,5,0,1,2],[4,5,0,1,2,3],[5,0,1,2,3,4]],"identity":0,"point_count":6,"action_table":[[0,1,2,3,4,5],[1,2,3,4,5,0],[2,3,4,5,0,1],[3,4,5,0,1,2],[4,5,0,1,2,3],[5,0,1,2,3,4]]}。請依 [triple_count, first_failure, compatible, certificate] 欄序回答。
(216, null, 是, all_g_h_x_checked)
Wave6根層核對=(216, null, 是, all_g_h_x_checked)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-compatibility-audit · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-compatibility-audit；資料={"group_table":[[0,1],[1,0]],"identity":0,"point_count":3,"action_table":[[0,1,2],[1,0,2]]}。請依 [triple_count, first_failure, compatible, certificate] 欄序回答。
(12, null, 是, all_g_h_x_checked)
Wave6根層核對=(12, null, 是, all_g_h_x_checked)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-compatibility-audit · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-compatibility-audit；資料={"group_table":[[0,1,2],[1,2,0],[2,0,1]],"identity":0,"point_count":4,"action_table":[[0,1,2,3],[1,2,0,3],[2,0,1,3]]}。請依 [triple_count, first_failure, compatible, certificate] 欄序回答。
(36, null, 是, all_g_h_x_checked)
Wave6根層核對=(36, null, 是, all_g_h_x_checked)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-compatibility-audit · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-compatibility-audit；資料={"group_table":[[0,1,2,3],[1,2,3,0],[2,3,0,1],[3,0,1,2]],"identity":0,"point_count":5,"action_table":[[0,1,2,3,4],[1,2,3,0,4],[2,3,0,1,4],[3,0,1,2,4]]}。請依 [triple_count, first_failure, compatible, certificate] 欄序回答。
(80, null, 是, all_g_h_x_checked)
Wave6根層核對=(80, null, 是, all_g_h_x_checked)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-compatibility-audit · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-compatibility-audit；資料={"group_table":[[0,1,2,3,4],[1,2,3,4,0],[2,3,4,0,1],[3,4,0,1,2],[4,0,1,2,3]],"identity":0,"point_count":6,"action_table":[[0,1,2,3,4,5],[1,2,3,4,0,5],[2,3,4,0,1,5],[3,4,0,1,2,5],[4,0,1,2,3,5]]}。請依 [triple_count, first_failure, compatible, certificate] 欄序回答。
(150, null, 是, all_g_h_x_checked)
Wave6根層核對=(150, null, 是, all_g_h_x_checked)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-compatibility-audit · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-compatibility-audit；資料={"group_table":[[0,1,2,3,4,5],[1,2,3,4,5,0],[2,3,4,5,0,1],[3,4,5,0,1,2],[4,5,0,1,2,3],[5,0,1,2,3,4]],"identity":0,"point_count":7,"action_table":[[0,1,2,3,4,5,6],[1,2,3,4,5,0,6],[2,3,4,5,0,1,6],[3,4,5,0,1,2,6],[4,5,0,1,2,3,6],[5,0,1,2,3,4,6]]}。請依 [triple_count, first_failure, compatible, certificate] 欄序回答。
(252, null, 是, all_g_h_x_checked)
Wave6根層核對=(252, null, 是, all_g_h_x_checked)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-compatibility-audit · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-compatibility-audit；資料={"group_table":[[0,1],[1,0]],"identity":0,"point_count":4,"action_table":[[0,1,2,3],[1,0,2,3]]}。請依 [triple_count, first_failure, compatible, certificate] 欄序回答。
(16, null, 是, all_g_h_x_checked)
Wave6根層核對=(16, null, 是, all_g_h_x_checked)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-compatibility-audit · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-compatibility-audit；資料={"group_table":[[0,1,2],[1,2,0],[2,0,1]],"identity":0,"point_count":5,"action_table":[[0,1,2,3,4],[1,2,0,3,4],[2,0,1,3,4]]}。請依 [triple_count, first_failure, compatible, certificate] 欄序回答。
(45, null, 是, all_g_h_x_checked)
Wave6根層核對=(45, null, 是, all_g_h_x_checked)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-compatibility-audit · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-compatibility-audit；資料={"group_table":[[0,1,2,3],[1,2,3,0],[2,3,0,1],[3,0,1,2]],"identity":0,"point_count":6,"action_table":[[0,1,2,3,4,5],[1,2,3,0,4,5],[2,3,0,1,4,5],[3,0,1,2,4,5]]}。請依 [triple_count, first_failure, compatible, certificate] 欄序回答。
(96, null, 是, all_g_h_x_checked)
Wave6根層核對=(96, null, 是, all_g_h_x_checked)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-compatibility-audit · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-compatibility-audit；資料={"group_table":[[0,1,2,3,4],[1,2,3,4,0],[2,3,4,0,1],[3,4,0,1,2],[4,0,1,2,3]],"identity":0,"point_count":7,"action_table":[[0,1,2,3,4,5,6],[1,2,3,4,0,5,6],[2,3,4,0,1,5,6],[3,4,0,1,2,5,6],[4,0,1,2,3,5,6]]}。請依 [triple_count, first_failure, compatible, certificate] 欄序回答。
(175, null, 是, all_g_h_x_checked)
Wave6根層核對=(175, null, 是, all_g_h_x_checked)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-compatibility-audit · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-compatibility-audit；資料={"group_table":[[0,1,2,3,4,5],[1,2,3,4,5,0],[2,3,4,5,0,1],[3,4,5,0,1,2],[4,5,0,1,2,3],[5,0,1,2,3,4]],"identity":0,"point_count":8,"action_table":[[0,1,2,3,4,5,6,7],[1,2,3,4,5,0,6,7],[2,3,4,5,0,1,6,7],[3,4,5,0,1,2,6,7],[4,5,0,1,2,3,6,7],[5,0,1,2,3,4,6,7]]}。請依 [triple_count, first_failure, compatible, certificate] 欄序回答。
(288, null, 是, all_g_h_x_checked)
Wave6根層核對=(288, null, 是, all_g_h_x_checked)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-compatibility-audit · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-compatibility-audit；資料={"group_table":[[0,1],[1,0]],"identity":0,"point_count":5,"action_table":[[0,1,2,3,4],[1,0,2,3,4]]}。請依 [triple_count, first_failure, compatible, certificate] 欄序回答。
(20, null, 是, all_g_h_x_checked)
Wave6根層核對=(20, null, 是, all_g_h_x_checked)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-compatibility-audit · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-compatibility-audit；資料={"group_table":[[0,1,2],[1,2,0],[2,0,1]],"identity":0,"point_count":6,"action_table":[[0,1,2,3,4,5],[1,2,0,3,4,5],[2,0,1,3,4,5]]}。請依 [triple_count, first_failure, compatible, certificate] 欄序回答。
(54, null, 是, all_g_h_x_checked)
Wave6根層核對=(54, null, 是, all_g_h_x_checked)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-compatibility-audit · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-compatibility-audit；資料={"group_table":[[0,1,2,3],[1,2,3,0],[2,3,0,1],[3,0,1,2]],"identity":0,"point_count":7,"action_table":[[0,1,2,3,4,5,6],[1,2,3,0,4,5,6],[2,3,0,1,4,5,6],[3,0,1,2,4,5,6]]}。請依 [triple_count, first_failure, compatible, certificate] 欄序回答。
(112, null, 是, all_g_h_x_checked)
Wave6根層核對=(112, null, 是, all_g_h_x_checked)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-compatibility-audit · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-compatibility-audit；資料={"group_table":[[0,1,2,3,4],[1,2,3,4,0],[2,3,4,0,1],[3,4,0,1,2],[4,0,1,2,3]],"identity":0,"point_count":8,"action_table":[[0,1,2,3,4,5,6,7],[1,2,3,4,0,5,6,7],[2,3,4,0,1,5,6,7],[3,4,0,1,2,5,6,7],[4,0,1,2,3,5,6,7]]}。請依 [triple_count, first_failure, compatible, certificate] 欄序回答。
(200, null, 是, all_g_h_x_checked)
Wave6根層核對=(200, null, 是, all_g_h_x_checked)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-compatibility-audit · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-compatibility-audit；資料={"group_table":[[0,1,2,3,4,5],[1,2,3,4,5,0],[2,3,4,5,0,1],[3,4,5,0,1,2],[4,5,0,1,2,3],[5,0,1,2,3,4]],"identity":0,"point_count":9,"action_table":[[0,1,2,3,4,5,6,7,8],[1,2,3,4,5,0,6,7,8],[2,3,4,5,0,1,6,7,8],[3,4,5,0,1,2,6,7,8],[4,5,0,1,2,3,6,7,8],[5,0,1,2,3,4,6,7,8]]}。請依 [triple_count, first_failure, compatible, certificate] 欄序回答。
(324, null, 是, all_g_h_x_checked)
Wave6根層核對=(324, null, 是, all_g_h_x_checked)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-compatibility-audit · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-compatibility-audit；資料={"group_table":[[0,1],[1,0]],"identity":0,"point_count":6,"action_table":[[0,1,2,3,4,5],[1,0,2,3,4,5]]}。請依 [triple_count, first_failure, compatible, certificate] 欄序回答。
(24, null, 是, all_g_h_x_checked)
Wave6根層核對=(24, null, 是, all_g_h_x_checked)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-compatibility-audit · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-compatibility-audit；資料={"group_table":[[0,1,2],[1,2,0],[2,0,1]],"identity":0,"point_count":7,"action_table":[[0,1,2,3,4,5,6],[1,2,0,3,4,5,6],[2,0,1,3,4,5,6]]}。請依 [triple_count, first_failure, compatible, certificate] 欄序回答。
(63, null, 是, all_g_h_x_checked)
Wave6根層核對=(63, null, 是, all_g_h_x_checked)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-compatibility-audit · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-compatibility-audit；資料={"group_table":[[0,1,2,3],[1,2,3,0],[2,3,0,1],[3,0,1,2]],"identity":0,"point_count":8,"action_table":[[0,1,2,3,4,5,6,7],[1,2,3,0,4,5,6,7],[2,3,0,1,4,5,6,7],[3,0,1,2,4,5,6,7]]}。請依 [triple_count, first_failure, compatible, certificate] 欄序回答。
(128, null, 是, all_g_h_x_checked)
Wave6根層核對=(128, null, 是, all_g_h_x_checked)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-compatibility-audit · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-compatibility-audit；資料={"group_table":[[0,1,2,3,4],[1,2,3,4,0],[2,3,4,0,1],[3,4,0,1,2],[4,0,1,2,3]],"identity":0,"point_count":9,"action_table":[[0,1,2,3,4,5,6,7,8],[1,2,3,4,0,5,6,7,8],[2,3,4,0,1,5,6,7,8],[3,4,0,1,2,5,6,7,8],[4,0,1,2,3,5,6,7,8]]}。請依 [triple_count, first_failure, compatible, certificate] 欄序回答。
(225, null, 是, all_g_h_x_checked)
Wave6根層核對=(225, null, 是, all_g_h_x_checked)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-compatibility-audit · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-compatibility-audit；資料={"group_table":[[0,1,2,3,4,5],[1,2,3,4,5,0],[2,3,4,5,0,1],[3,4,5,0,1,2],[4,5,0,1,2,3],[5,0,1,2,3,4]],"identity":0,"point_count":10,"action_table":[[0,1,2,3,4,5,6,7,8,9],[1,2,3,4,5,0,6,7,8,9],[2,3,4,5,0,1,6,7,8,9],[3,4,5,0,1,2,6,7,8,9],[4,5,0,1,2,3,6,7,8,9],[5,0,1,2,3,4,6,7,8,9]]}。請依 [triple_count, first_failure, compatible, certificate] 欄序回答。
(360, null, 是, all_g_h_x_checked)
Wave6根層核對=(360, null, 是, all_g_h_x_checked)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-compatibility-audit · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-nonproperty-boundary；資料={"group_table":[[0,1],[1,0]],"identity":0,"point_count":2,"action_table":[[0,1],[1,0]]}。請依 [valid_action, faithful_claim, free_claim, transitive_claim, boundary] 欄序回答。
三個否是不作faithful、free或transitive性質聲稱，不表示這些性質已被證明為假。
(是, 否, 否, 否, valid_action_does_not_automatically_claim_faithful_free_or_transitive)
Wave6根層核對=(是, 否, 否, 否, valid_action_does_not_automatically_claim_faithful_free_or_transitive)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-nonproperty-boundary · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-nonproperty-boundary；資料={"group_table":[[0,1,2],[1,2,0],[2,0,1]],"identity":0,"point_count":3,"action_table":[[0,1,2],[1,2,0],[2,0,1]]}。請依 [valid_action, faithful_claim, free_claim, transitive_claim, boundary] 欄序回答。
三個否是不作faithful、free或transitive性質聲稱，不表示這些性質已被證明為假。
(是, 否, 否, 否, valid_action_does_not_automatically_claim_faithful_free_or_transitive)
Wave6根層核對=(是, 否, 否, 否, valid_action_does_not_automatically_claim_faithful_free_or_transitive)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-nonproperty-boundary · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-nonproperty-boundary；資料={"group_table":[[0,1,2,3],[1,2,3,0],[2,3,0,1],[3,0,1,2]],"identity":0,"point_count":4,"action_table":[[0,1,2,3],[1,2,3,0],[2,3,0,1],[3,0,1,2]]}。請依 [valid_action, faithful_claim, free_claim, transitive_claim, boundary] 欄序回答。
三個否是不作faithful、free或transitive性質聲稱，不表示這些性質已被證明為假。
(是, 否, 否, 否, valid_action_does_not_automatically_claim_faithful_free_or_transitive)
Wave6根層核對=(是, 否, 否, 否, valid_action_does_not_automatically_claim_faithful_free_or_transitive)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-nonproperty-boundary · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-nonproperty-boundary；資料={"group_table":[[0,1,2,3,4],[1,2,3,4,0],[2,3,4,0,1],[3,4,0,1,2],[4,0,1,2,3]],"identity":0,"point_count":5,"action_table":[[0,1,2,3,4],[1,2,3,4,0],[2,3,4,0,1],[3,4,0,1,2],[4,0,1,2,3]]}。請依 [valid_action, faithful_claim, free_claim, transitive_claim, boundary] 欄序回答。
三個否是不作faithful、free或transitive性質聲稱，不表示這些性質已被證明為假。
(是, 否, 否, 否, valid_action_does_not_automatically_claim_faithful_free_or_transitive)
Wave6根層核對=(是, 否, 否, 否, valid_action_does_not_automatically_claim_faithful_free_or_transitive)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-nonproperty-boundary · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-nonproperty-boundary；資料={"group_table":[[0,1,2,3,4,5],[1,2,3,4,5,0],[2,3,4,5,0,1],[3,4,5,0,1,2],[4,5,0,1,2,3],[5,0,1,2,3,4]],"identity":0,"point_count":6,"action_table":[[0,1,2,3,4,5],[1,2,3,4,5,0],[2,3,4,5,0,1],[3,4,5,0,1,2],[4,5,0,1,2,3],[5,0,1,2,3,4]]}。請依 [valid_action, faithful_claim, free_claim, transitive_claim, boundary] 欄序回答。
三個否是不作faithful、free或transitive性質聲稱，不表示這些性質已被證明為假。
(是, 否, 否, 否, valid_action_does_not_automatically_claim_faithful_free_or_transitive)
Wave6根層核對=(是, 否, 否, 否, valid_action_does_not_automatically_claim_faithful_free_or_transitive)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-nonproperty-boundary · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-nonproperty-boundary；資料={"group_table":[[0,1],[1,0]],"identity":0,"point_count":3,"action_table":[[0,1,2],[1,0,2]]}。請依 [valid_action, faithful_claim, free_claim, transitive_claim, boundary] 欄序回答。
三個否是不作faithful、free或transitive性質聲稱，不表示這些性質已被證明為假。
(是, 否, 否, 否, valid_action_does_not_automatically_claim_faithful_free_or_transitive)
Wave6根層核對=(是, 否, 否, 否, valid_action_does_not_automatically_claim_faithful_free_or_transitive)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-nonproperty-boundary · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-nonproperty-boundary；資料={"group_table":[[0,1,2],[1,2,0],[2,0,1]],"identity":0,"point_count":4,"action_table":[[0,1,2,3],[1,2,0,3],[2,0,1,3]]}。請依 [valid_action, faithful_claim, free_claim, transitive_claim, boundary] 欄序回答。
三個否是不作faithful、free或transitive性質聲稱，不表示這些性質已被證明為假。
(是, 否, 否, 否, valid_action_does_not_automatically_claim_faithful_free_or_transitive)
Wave6根層核對=(是, 否, 否, 否, valid_action_does_not_automatically_claim_faithful_free_or_transitive)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-nonproperty-boundary · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-nonproperty-boundary；資料={"group_table":[[0,1,2,3],[1,2,3,0],[2,3,0,1],[3,0,1,2]],"identity":0,"point_count":5,"action_table":[[0,1,2,3,4],[1,2,3,0,4],[2,3,0,1,4],[3,0,1,2,4]]}。請依 [valid_action, faithful_claim, free_claim, transitive_claim, boundary] 欄序回答。
三個否是不作faithful、free或transitive性質聲稱，不表示這些性質已被證明為假。
(是, 否, 否, 否, valid_action_does_not_automatically_claim_faithful_free_or_transitive)
Wave6根層核對=(是, 否, 否, 否, valid_action_does_not_automatically_claim_faithful_free_or_transitive)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-nonproperty-boundary · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-nonproperty-boundary；資料={"group_table":[[0,1,2,3,4],[1,2,3,4,0],[2,3,4,0,1],[3,4,0,1,2],[4,0,1,2,3]],"identity":0,"point_count":6,"action_table":[[0,1,2,3,4,5],[1,2,3,4,0,5],[2,3,4,0,1,5],[3,4,0,1,2,5],[4,0,1,2,3,5]]}。請依 [valid_action, faithful_claim, free_claim, transitive_claim, boundary] 欄序回答。
三個否是不作faithful、free或transitive性質聲稱，不表示這些性質已被證明為假。
(是, 否, 否, 否, valid_action_does_not_automatically_claim_faithful_free_or_transitive)
Wave6根層核對=(是, 否, 否, 否, valid_action_does_not_automatically_claim_faithful_free_or_transitive)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-nonproperty-boundary · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-nonproperty-boundary；資料={"group_table":[[0,1,2,3,4,5],[1,2,3,4,5,0],[2,3,4,5,0,1],[3,4,5,0,1,2],[4,5,0,1,2,3],[5,0,1,2,3,4]],"identity":0,"point_count":7,"action_table":[[0,1,2,3,4,5,6],[1,2,3,4,5,0,6],[2,3,4,5,0,1,6],[3,4,5,0,1,2,6],[4,5,0,1,2,3,6],[5,0,1,2,3,4,6]]}。請依 [valid_action, faithful_claim, free_claim, transitive_claim, boundary] 欄序回答。
三個否是不作faithful、free或transitive性質聲稱，不表示這些性質已被證明為假。
(是, 否, 否, 否, valid_action_does_not_automatically_claim_faithful_free_or_transitive)
Wave6根層核對=(是, 否, 否, 否, valid_action_does_not_automatically_claim_faithful_free_or_transitive)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-nonproperty-boundary · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-nonproperty-boundary；資料={"group_table":[[0,1],[1,0]],"identity":0,"point_count":4,"action_table":[[0,1,2,3],[1,0,2,3]]}。請依 [valid_action, faithful_claim, free_claim, transitive_claim, boundary] 欄序回答。
三個否是不作faithful、free或transitive性質聲稱，不表示這些性質已被證明為假。
(是, 否, 否, 否, valid_action_does_not_automatically_claim_faithful_free_or_transitive)
Wave6根層核對=(是, 否, 否, 否, valid_action_does_not_automatically_claim_faithful_free_or_transitive)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-nonproperty-boundary · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-nonproperty-boundary；資料={"group_table":[[0,1,2],[1,2,0],[2,0,1]],"identity":0,"point_count":5,"action_table":[[0,1,2,3,4],[1,2,0,3,4],[2,0,1,3,4]]}。請依 [valid_action, faithful_claim, free_claim, transitive_claim, boundary] 欄序回答。
三個否是不作faithful、free或transitive性質聲稱，不表示這些性質已被證明為假。
(是, 否, 否, 否, valid_action_does_not_automatically_claim_faithful_free_or_transitive)
Wave6根層核對=(是, 否, 否, 否, valid_action_does_not_automatically_claim_faithful_free_or_transitive)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-nonproperty-boundary · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-nonproperty-boundary；資料={"group_table":[[0,1,2,3],[1,2,3,0],[2,3,0,1],[3,0,1,2]],"identity":0,"point_count":6,"action_table":[[0,1,2,3,4,5],[1,2,3,0,4,5],[2,3,0,1,4,5],[3,0,1,2,4,5]]}。請依 [valid_action, faithful_claim, free_claim, transitive_claim, boundary] 欄序回答。
三個否是不作faithful、free或transitive性質聲稱，不表示這些性質已被證明為假。
(是, 否, 否, 否, valid_action_does_not_automatically_claim_faithful_free_or_transitive)
Wave6根層核對=(是, 否, 否, 否, valid_action_does_not_automatically_claim_faithful_free_or_transitive)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-nonproperty-boundary · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-nonproperty-boundary；資料={"group_table":[[0,1,2,3,4],[1,2,3,4,0],[2,3,4,0,1],[3,4,0,1,2],[4,0,1,2,3]],"identity":0,"point_count":7,"action_table":[[0,1,2,3,4,5,6],[1,2,3,4,0,5,6],[2,3,4,0,1,5,6],[3,4,0,1,2,5,6],[4,0,1,2,3,5,6]]}。請依 [valid_action, faithful_claim, free_claim, transitive_claim, boundary] 欄序回答。
三個否是不作faithful、free或transitive性質聲稱，不表示這些性質已被證明為假。
(是, 否, 否, 否, valid_action_does_not_automatically_claim_faithful_free_or_transitive)
Wave6根層核對=(是, 否, 否, 否, valid_action_does_not_automatically_claim_faithful_free_or_transitive)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-nonproperty-boundary · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-nonproperty-boundary；資料={"group_table":[[0,1,2,3,4,5],[1,2,3,4,5,0],[2,3,4,5,0,1],[3,4,5,0,1,2],[4,5,0,1,2,3],[5,0,1,2,3,4]],"identity":0,"point_count":8,"action_table":[[0,1,2,3,4,5,6,7],[1,2,3,4,5,0,6,7],[2,3,4,5,0,1,6,7],[3,4,5,0,1,2,6,7],[4,5,0,1,2,3,6,7],[5,0,1,2,3,4,6,7]]}。請依 [valid_action, faithful_claim, free_claim, transitive_claim, boundary] 欄序回答。
三個否是不作faithful、free或transitive性質聲稱，不表示這些性質已被證明為假。
(是, 否, 否, 否, valid_action_does_not_automatically_claim_faithful_free_or_transitive)
Wave6根層核對=(是, 否, 否, 否, valid_action_does_not_automatically_claim_faithful_free_or_transitive)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-nonproperty-boundary · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-nonproperty-boundary；資料={"group_table":[[0,1],[1,0]],"identity":0,"point_count":5,"action_table":[[0,1,2,3,4],[1,0,2,3,4]]}。請依 [valid_action, faithful_claim, free_claim, transitive_claim, boundary] 欄序回答。
三個否是不作faithful、free或transitive性質聲稱，不表示這些性質已被證明為假。
(是, 否, 否, 否, valid_action_does_not_automatically_claim_faithful_free_or_transitive)
Wave6根層核對=(是, 否, 否, 否, valid_action_does_not_automatically_claim_faithful_free_or_transitive)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-nonproperty-boundary · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-nonproperty-boundary；資料={"group_table":[[0,1,2],[1,2,0],[2,0,1]],"identity":0,"point_count":6,"action_table":[[0,1,2,3,4,5],[1,2,0,3,4,5],[2,0,1,3,4,5]]}。請依 [valid_action, faithful_claim, free_claim, transitive_claim, boundary] 欄序回答。
三個否是不作faithful、free或transitive性質聲稱，不表示這些性質已被證明為假。
(是, 否, 否, 否, valid_action_does_not_automatically_claim_faithful_free_or_transitive)
Wave6根層核對=(是, 否, 否, 否, valid_action_does_not_automatically_claim_faithful_free_or_transitive)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-nonproperty-boundary · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-nonproperty-boundary；資料={"group_table":[[0,1,2,3],[1,2,3,0],[2,3,0,1],[3,0,1,2]],"identity":0,"point_count":7,"action_table":[[0,1,2,3,4,5,6],[1,2,3,0,4,5,6],[2,3,0,1,4,5,6],[3,0,1,2,4,5,6]]}。請依 [valid_action, faithful_claim, free_claim, transitive_claim, boundary] 欄序回答。
三個否是不作faithful、free或transitive性質聲稱，不表示這些性質已被證明為假。
(是, 否, 否, 否, valid_action_does_not_automatically_claim_faithful_free_or_transitive)
Wave6根層核對=(是, 否, 否, 否, valid_action_does_not_automatically_claim_faithful_free_or_transitive)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-nonproperty-boundary · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-nonproperty-boundary；資料={"group_table":[[0,1,2,3,4],[1,2,3,4,0],[2,3,4,0,1],[3,4,0,1,2],[4,0,1,2,3]],"identity":0,"point_count":8,"action_table":[[0,1,2,3,4,5,6,7],[1,2,3,4,0,5,6,7],[2,3,4,0,1,5,6,7],[3,4,0,1,2,5,6,7],[4,0,1,2,3,5,6,7]]}。請依 [valid_action, faithful_claim, free_claim, transitive_claim, boundary] 欄序回答。
三個否是不作faithful、free或transitive性質聲稱，不表示這些性質已被證明為假。
(是, 否, 否, 否, valid_action_does_not_automatically_claim_faithful_free_or_transitive)
Wave6根層核對=(是, 否, 否, 否, valid_action_does_not_automatically_claim_faithful_free_or_transitive)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-nonproperty-boundary · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-nonproperty-boundary；資料={"group_table":[[0,1,2,3,4,5],[1,2,3,4,5,0],[2,3,4,5,0,1],[3,4,5,0,1,2],[4,5,0,1,2,3],[5,0,1,2,3,4]],"identity":0,"point_count":9,"action_table":[[0,1,2,3,4,5,6,7,8],[1,2,3,4,5,0,6,7,8],[2,3,4,5,0,1,6,7,8],[3,4,5,0,1,2,6,7,8],[4,5,0,1,2,3,6,7,8],[5,0,1,2,3,4,6,7,8]]}。請依 [valid_action, faithful_claim, free_claim, transitive_claim, boundary] 欄序回答。
三個否是不作faithful、free或transitive性質聲稱，不表示這些性質已被證明為假。
(是, 否, 否, 否, valid_action_does_not_automatically_claim_faithful_free_or_transitive)
Wave6根層核對=(是, 否, 否, 否, valid_action_does_not_automatically_claim_faithful_free_or_transitive)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-nonproperty-boundary · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-nonproperty-boundary；資料={"group_table":[[0,1],[1,0]],"identity":0,"point_count":6,"action_table":[[0,1,2,3,4,5],[1,0,2,3,4,5]]}。請依 [valid_action, faithful_claim, free_claim, transitive_claim, boundary] 欄序回答。
三個否是不作faithful、free或transitive性質聲稱，不表示這些性質已被證明為假。
(是, 否, 否, 否, valid_action_does_not_automatically_claim_faithful_free_or_transitive)
Wave6根層核對=(是, 否, 否, 否, valid_action_does_not_automatically_claim_faithful_free_or_transitive)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-nonproperty-boundary · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-nonproperty-boundary；資料={"group_table":[[0,1,2],[1,2,0],[2,0,1]],"identity":0,"point_count":7,"action_table":[[0,1,2,3,4,5,6],[1,2,0,3,4,5,6],[2,0,1,3,4,5,6]]}。請依 [valid_action, faithful_claim, free_claim, transitive_claim, boundary] 欄序回答。
三個否是不作faithful、free或transitive性質聲稱，不表示這些性質已被證明為假。
(是, 否, 否, 否, valid_action_does_not_automatically_claim_faithful_free_or_transitive)
Wave6根層核對=(是, 否, 否, 否, valid_action_does_not_automatically_claim_faithful_free_or_transitive)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-nonproperty-boundary · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-nonproperty-boundary；資料={"group_table":[[0,1,2,3],[1,2,3,0],[2,3,0,1],[3,0,1,2]],"identity":0,"point_count":8,"action_table":[[0,1,2,3,4,5,6,7],[1,2,3,0,4,5,6,7],[2,3,0,1,4,5,6,7],[3,0,1,2,4,5,6,7]]}。請依 [valid_action, faithful_claim, free_claim, transitive_claim, boundary] 欄序回答。
三個否是不作faithful、free或transitive性質聲稱，不表示這些性質已被證明為假。
(是, 否, 否, 否, valid_action_does_not_automatically_claim_faithful_free_or_transitive)
Wave6根層核對=(是, 否, 否, 否, valid_action_does_not_automatically_claim_faithful_free_or_transitive)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-nonproperty-boundary · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-nonproperty-boundary；資料={"group_table":[[0,1,2,3,4],[1,2,3,4,0],[2,3,4,0,1],[3,4,0,1,2],[4,0,1,2,3]],"identity":0,"point_count":9,"action_table":[[0,1,2,3,4,5,6,7,8],[1,2,3,4,0,5,6,7,8],[2,3,4,0,1,5,6,7,8],[3,4,0,1,2,5,6,7,8],[4,0,1,2,3,5,6,7,8]]}。請依 [valid_action, faithful_claim, free_claim, transitive_claim, boundary] 欄序回答。
三個否是不作faithful、free或transitive性質聲稱，不表示這些性質已被證明為假。
(是, 否, 否, 否, valid_action_does_not_automatically_claim_faithful_free_or_transitive)
Wave6根層核對=(是, 否, 否, 否, valid_action_does_not_automatically_claim_faithful_free_or_transitive)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-nonproperty-boundary · candidate
完整有限群Cayley table、完整有限集合與total action table。操作=groupaction-nonproperty-boundary；資料={"group_table":[[0,1,2,3,4,5],[1,2,3,4,5,0],[2,3,4,5,0,1],[3,4,5,0,1,2],[4,5,0,1,2,3],[5,0,1,2,3,4]],"identity":0,"point_count":10,"action_table":[[0,1,2,3,4,5,6,7,8,9],[1,2,3,4,5,0,6,7,8,9],[2,3,4,5,0,1,6,7,8,9],[3,4,5,0,1,2,6,7,8,9],[4,5,0,1,2,3,6,7,8,9],[5,0,1,2,3,4,6,7,8,9]]}。請依 [valid_action, faithful_claim, free_claim, transitive_claim, boundary] 欄序回答。
三個否是不作faithful、free或transitive性質聲稱，不表示這些性質已被證明為假。
(是, 否, 否, 否, valid_action_does_not_automatically_claim_faithful_free_or_transitive)
Wave6根層核對=(是, 否, 否, 否, valid_action_does_not_automatically_claim_faithful_free_or_transitive)；依完整明示資料獨立重算；全稱核e作用與(gh)作用相容性；有限抽樣pairs不足；每個群元素誘導排列，但有效作用不自動宣稱faithful、free或transitive。
有限群作用 · qf-mod38-groupaction-nonproperty-boundary · candidate