有限群作用的穩定子群基礎 · 脈衝 R01
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-20261109-r01-finite-group-stabilizer-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。
欄序與來源綁定資料
1. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-stabilizer-of-point；資料={"group_table":[[0,1],[1,0]],"identity":0,"point_count":2,"action_table":[[0,1],[1,0]],"point":0}。請依 [point, stabilizer, stabilizer_order, full_enumeration_certificate, certificate] 欄序回答。
查看答案與解釋
(0, [0], 1, 是, all_group_elements_checked)
Wave6第三層核對=(0, [0], 1, 是, all_group_elements_checked)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-stabilizer-of-point · candidate
2. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-stabilizer-of-point；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]],"point":1}。請依 [point, stabilizer, stabilizer_order, full_enumeration_certificate, certificate] 欄序回答。
查看答案與解釋
(1, [0], 1, 是, all_group_elements_checked)
Wave6第三層核對=(1, [0], 1, 是, all_group_elements_checked)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-stabilizer-of-point · candidate
3. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-stabilizer-of-point；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]],"point":2}。請依 [point, stabilizer, stabilizer_order, full_enumeration_certificate, certificate] 欄序回答。
查看答案與解釋
(2, [0], 1, 是, all_group_elements_checked)
Wave6第三層核對=(2, [0], 1, 是, all_group_elements_checked)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-stabilizer-of-point · candidate
4. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-stabilizer-of-point；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]],"point":3}。請依 [point, stabilizer, stabilizer_order, full_enumeration_certificate, certificate] 欄序回答。
查看答案與解釋
(3, [0], 1, 是, all_group_elements_checked)
Wave6第三層核對=(3, [0], 1, 是, all_group_elements_checked)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-stabilizer-of-point · candidate
5. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-stabilizer-of-point；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]],"point":4}。請依 [point, stabilizer, stabilizer_order, full_enumeration_certificate, certificate] 欄序回答。
查看答案與解釋
(4, [0], 1, 是, all_group_elements_checked)
Wave6第三層核對=(4, [0], 1, 是, all_group_elements_checked)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-stabilizer-of-point · candidate
6. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-stabilizer-of-point；資料={"group_table":[[0,1],[1,0]],"identity":0,"point_count":3,"action_table":[[0,1,2],[1,0,2]],"point":2}。請依 [point, stabilizer, stabilizer_order, full_enumeration_certificate, certificate] 欄序回答。
查看答案與解釋
(2, [0, 1], 2, 是, all_group_elements_checked)
Wave6第三層核對=(2, [0, 1], 2, 是, all_group_elements_checked)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-stabilizer-of-point · candidate
7. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-stabilizer-of-point；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]],"point":2}。請依 [point, stabilizer, stabilizer_order, full_enumeration_certificate, certificate] 欄序回答。
查看答案與解釋
(2, [0], 1, 是, all_group_elements_checked)
Wave6第三層核對=(2, [0], 1, 是, all_group_elements_checked)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-stabilizer-of-point · candidate
8. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-stabilizer-of-point；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]],"point":2}。請依 [point, stabilizer, stabilizer_order, full_enumeration_certificate, certificate] 欄序回答。
查看答案與解釋
(2, [0], 1, 是, all_group_elements_checked)
Wave6第三層核對=(2, [0], 1, 是, all_group_elements_checked)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-stabilizer-of-point · candidate
9. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-stabilizer-of-point；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]],"point":2}。請依 [point, stabilizer, stabilizer_order, full_enumeration_certificate, certificate] 欄序回答。
查看答案與解釋
(2, [0], 1, 是, all_group_elements_checked)
Wave6第三層核對=(2, [0], 1, 是, all_group_elements_checked)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-stabilizer-of-point · candidate
10. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-stabilizer-of-point；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]],"point":2}。請依 [point, stabilizer, stabilizer_order, full_enumeration_certificate, certificate] 欄序回答。
查看答案與解釋
(2, [0], 1, 是, all_group_elements_checked)
Wave6第三層核對=(2, [0], 1, 是, all_group_elements_checked)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-stabilizer-of-point · candidate
11. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-stabilizer-of-point；資料={"group_table":[[0,1],[1,0]],"identity":0,"point_count":4,"action_table":[[0,1,2,3],[1,0,2,3]],"point":2}。請依 [point, stabilizer, stabilizer_order, full_enumeration_certificate, certificate] 欄序回答。
查看答案與解釋
(2, [0, 1], 2, 是, all_group_elements_checked)
Wave6第三層核對=(2, [0, 1], 2, 是, all_group_elements_checked)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-stabilizer-of-point · candidate
12. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-stabilizer-of-point；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]],"point":1}。請依 [point, stabilizer, stabilizer_order, full_enumeration_certificate, certificate] 欄序回答。
查看答案與解釋
(1, [0], 1, 是, all_group_elements_checked)
Wave6第三層核對=(1, [0], 1, 是, all_group_elements_checked)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-stabilizer-of-point · candidate
13. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-stabilizer-of-point；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]],"point":0}。請依 [point, stabilizer, stabilizer_order, full_enumeration_certificate, certificate] 欄序回答。
查看答案與解釋
(0, [0], 1, 是, all_group_elements_checked)
Wave6第三層核對=(0, [0], 1, 是, all_group_elements_checked)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-stabilizer-of-point · candidate
14. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-stabilizer-of-point；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]],"point":6}。請依 [point, stabilizer, stabilizer_order, full_enumeration_certificate, certificate] 欄序回答。
查看答案與解釋
(6, [0, 1, 2, 3, 4], 5, 是, all_group_elements_checked)
Wave6第三層核對=(6, [0, 1, 2, 3, 4], 5, 是, all_group_elements_checked)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-stabilizer-of-point · candidate
15. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-stabilizer-of-point；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]],"point":6}。請依 [point, stabilizer, stabilizer_order, full_enumeration_certificate, certificate] 欄序回答。
查看答案與解釋
(6, [0, 1, 2, 3, 4, 5], 6, 是, all_group_elements_checked)
Wave6第三層核對=(6, [0, 1, 2, 3, 4, 5], 6, 是, all_group_elements_checked)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-stabilizer-of-point · candidate
16. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-stabilizer-of-point；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]],"point":0}。請依 [point, stabilizer, stabilizer_order, full_enumeration_certificate, certificate] 欄序回答。
查看答案與解釋
(0, [0], 1, 是, all_group_elements_checked)
Wave6第三層核對=(0, [0], 1, 是, all_group_elements_checked)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-stabilizer-of-point · candidate
17. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-stabilizer-of-point；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]],"point":4}。請依 [point, stabilizer, stabilizer_order, full_enumeration_certificate, certificate] 欄序回答。
查看答案與解釋
(4, [0, 1, 2], 3, 是, all_group_elements_checked)
Wave6第三層核對=(4, [0, 1, 2], 3, 是, all_group_elements_checked)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-stabilizer-of-point · candidate
18. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-stabilizer-of-point；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]],"point":3}。請依 [point, stabilizer, stabilizer_order, full_enumeration_certificate, certificate] 欄序回答。
查看答案與解釋
(3, [0], 1, 是, all_group_elements_checked)
Wave6第三層核對=(3, [0], 1, 是, all_group_elements_checked)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-stabilizer-of-point · candidate
19. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-stabilizer-of-point；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]],"point":2}。請依 [point, stabilizer, stabilizer_order, full_enumeration_certificate, certificate] 欄序回答。
查看答案與解釋
(2, [0], 1, 是, all_group_elements_checked)
Wave6第三層核對=(2, [0], 1, 是, all_group_elements_checked)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-stabilizer-of-point · candidate
20. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-stabilizer-of-point；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]],"point":1}。請依 [point, stabilizer, stabilizer_order, full_enumeration_certificate, certificate] 欄序回答。
查看答案與解釋
(1, [0], 1, 是, all_group_elements_checked)
Wave6第三層核對=(1, [0], 1, 是, all_group_elements_checked)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-stabilizer-of-point · candidate
21. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-stabilizer-of-point；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]],"point":2}。請依 [point, stabilizer, stabilizer_order, full_enumeration_certificate, certificate] 欄序回答。
查看答案與解釋
(2, [0, 1], 2, 是, all_group_elements_checked)
Wave6第三層核對=(2, [0, 1], 2, 是, all_group_elements_checked)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-stabilizer-of-point · candidate
22. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-stabilizer-of-point；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]],"point":0}。請依 [point, stabilizer, stabilizer_order, full_enumeration_certificate, certificate] 欄序回答。
查看答案與解釋
(0, [0], 1, 是, all_group_elements_checked)
Wave6第三層核對=(0, [0], 1, 是, all_group_elements_checked)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-stabilizer-of-point · candidate
23. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-stabilizer-of-point；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]],"point":6}。請依 [point, stabilizer, stabilizer_order, full_enumeration_certificate, certificate] 欄序回答。
查看答案與解釋
(6, [0, 1, 2, 3], 4, 是, all_group_elements_checked)
Wave6第三層核對=(6, [0, 1, 2, 3], 4, 是, all_group_elements_checked)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-stabilizer-of-point · candidate
24. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-stabilizer-of-point；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]],"point":5}。請依 [point, stabilizer, stabilizer_order, full_enumeration_certificate, certificate] 欄序回答。
查看答案與解釋
(5, [0, 1, 2, 3, 4], 5, 是, all_group_elements_checked)
Wave6第三層核對=(5, [0, 1, 2, 3, 4], 5, 是, all_group_elements_checked)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-stabilizer-of-point · candidate
25. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-stabilizer-of-point；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]],"point":4}。請依 [point, stabilizer, stabilizer_order, full_enumeration_certificate, certificate] 欄序回答。
查看答案與解釋
(4, [0], 1, 是, all_group_elements_checked)
Wave6第三層核對=(4, [0], 1, 是, all_group_elements_checked)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-stabilizer-of-point · candidate
26. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-subgroup-certificate；資料={"group_table":[[0,1],[1,0]],"identity":0,"point_count":2,"action_table":[[0,1],[1,0]],"point":0}。請依 [stabilizer, identity, contains_identity, product_closed, inverse_closed, subgroup, certificate] 欄序回答。
查看答案與解釋
([0], 0, 是, 是, 是, 是, identity_product_inverse_closure)
Wave6第三層核對=([0], 0, 是, 是, 是, 是, identity_product_inverse_closure)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-subgroup-certificate · candidate
27. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-subgroup-certificate；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]],"point":1}。請依 [stabilizer, identity, contains_identity, product_closed, inverse_closed, subgroup, certificate] 欄序回答。
查看答案與解釋
([0], 0, 是, 是, 是, 是, identity_product_inverse_closure)
Wave6第三層核對=([0], 0, 是, 是, 是, 是, identity_product_inverse_closure)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-subgroup-certificate · candidate
28. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-subgroup-certificate；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]],"point":2}。請依 [stabilizer, identity, contains_identity, product_closed, inverse_closed, subgroup, certificate] 欄序回答。
查看答案與解釋
([0], 0, 是, 是, 是, 是, identity_product_inverse_closure)
Wave6第三層核對=([0], 0, 是, 是, 是, 是, identity_product_inverse_closure)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-subgroup-certificate · candidate
29. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-subgroup-certificate；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]],"point":3}。請依 [stabilizer, identity, contains_identity, product_closed, inverse_closed, subgroup, certificate] 欄序回答。
查看答案與解釋
([0], 0, 是, 是, 是, 是, identity_product_inverse_closure)
Wave6第三層核對=([0], 0, 是, 是, 是, 是, identity_product_inverse_closure)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-subgroup-certificate · candidate
30. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-subgroup-certificate；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]],"point":4}。請依 [stabilizer, identity, contains_identity, product_closed, inverse_closed, subgroup, certificate] 欄序回答。
查看答案與解釋
([0], 0, 是, 是, 是, 是, identity_product_inverse_closure)
Wave6第三層核對=([0], 0, 是, 是, 是, 是, identity_product_inverse_closure)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-subgroup-certificate · candidate
31. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-subgroup-certificate；資料={"group_table":[[0,1],[1,0]],"identity":0,"point_count":3,"action_table":[[0,1,2],[1,0,2]],"point":2}。請依 [stabilizer, identity, contains_identity, product_closed, inverse_closed, subgroup, certificate] 欄序回答。
查看答案與解釋
([0, 1], 0, 是, 是, 是, 是, identity_product_inverse_closure)
Wave6第三層核對=([0, 1], 0, 是, 是, 是, 是, identity_product_inverse_closure)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-subgroup-certificate · candidate
32. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-subgroup-certificate；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]],"point":2}。請依 [stabilizer, identity, contains_identity, product_closed, inverse_closed, subgroup, certificate] 欄序回答。
查看答案與解釋
([0], 0, 是, 是, 是, 是, identity_product_inverse_closure)
Wave6第三層核對=([0], 0, 是, 是, 是, 是, identity_product_inverse_closure)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-subgroup-certificate · candidate
33. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-subgroup-certificate；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]],"point":2}。請依 [stabilizer, identity, contains_identity, product_closed, inverse_closed, subgroup, certificate] 欄序回答。
查看答案與解釋
([0], 0, 是, 是, 是, 是, identity_product_inverse_closure)
Wave6第三層核對=([0], 0, 是, 是, 是, 是, identity_product_inverse_closure)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-subgroup-certificate · candidate
34. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-subgroup-certificate；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]],"point":2}。請依 [stabilizer, identity, contains_identity, product_closed, inverse_closed, subgroup, certificate] 欄序回答。
查看答案與解釋
([0], 0, 是, 是, 是, 是, identity_product_inverse_closure)
Wave6第三層核對=([0], 0, 是, 是, 是, 是, identity_product_inverse_closure)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-subgroup-certificate · candidate
35. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-subgroup-certificate；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]],"point":2}。請依 [stabilizer, identity, contains_identity, product_closed, inverse_closed, subgroup, certificate] 欄序回答。
查看答案與解釋
([0], 0, 是, 是, 是, 是, identity_product_inverse_closure)
Wave6第三層核對=([0], 0, 是, 是, 是, 是, identity_product_inverse_closure)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-subgroup-certificate · candidate
36. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-subgroup-certificate；資料={"group_table":[[0,1],[1,0]],"identity":0,"point_count":4,"action_table":[[0,1,2,3],[1,0,2,3]],"point":2}。請依 [stabilizer, identity, contains_identity, product_closed, inverse_closed, subgroup, certificate] 欄序回答。
查看答案與解釋
([0, 1], 0, 是, 是, 是, 是, identity_product_inverse_closure)
Wave6第三層核對=([0, 1], 0, 是, 是, 是, 是, identity_product_inverse_closure)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-subgroup-certificate · candidate
37. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-subgroup-certificate；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]],"point":1}。請依 [stabilizer, identity, contains_identity, product_closed, inverse_closed, subgroup, certificate] 欄序回答。
查看答案與解釋
([0], 0, 是, 是, 是, 是, identity_product_inverse_closure)
Wave6第三層核對=([0], 0, 是, 是, 是, 是, identity_product_inverse_closure)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-subgroup-certificate · candidate
38. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-subgroup-certificate；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]],"point":0}。請依 [stabilizer, identity, contains_identity, product_closed, inverse_closed, subgroup, certificate] 欄序回答。
查看答案與解釋
([0], 0, 是, 是, 是, 是, identity_product_inverse_closure)
Wave6第三層核對=([0], 0, 是, 是, 是, 是, identity_product_inverse_closure)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-subgroup-certificate · candidate
39. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-subgroup-certificate；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]],"point":6}。請依 [stabilizer, identity, contains_identity, product_closed, inverse_closed, subgroup, certificate] 欄序回答。
查看答案與解釋
([0, 1, 2, 3, 4], 0, 是, 是, 是, 是, identity_product_inverse_closure)
Wave6第三層核對=([0, 1, 2, 3, 4], 0, 是, 是, 是, 是, identity_product_inverse_closure)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-subgroup-certificate · candidate
40. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-subgroup-certificate；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]],"point":6}。請依 [stabilizer, identity, contains_identity, product_closed, inverse_closed, subgroup, certificate] 欄序回答。
查看答案與解釋
([0, 1, 2, 3, 4, 5], 0, 是, 是, 是, 是, identity_product_inverse_closure)
Wave6第三層核對=([0, 1, 2, 3, 4, 5], 0, 是, 是, 是, 是, identity_product_inverse_closure)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-subgroup-certificate · candidate
41. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-subgroup-certificate；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]],"point":0}。請依 [stabilizer, identity, contains_identity, product_closed, inverse_closed, subgroup, certificate] 欄序回答。
查看答案與解釋
([0], 0, 是, 是, 是, 是, identity_product_inverse_closure)
Wave6第三層核對=([0], 0, 是, 是, 是, 是, identity_product_inverse_closure)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-subgroup-certificate · candidate
42. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-subgroup-certificate；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]],"point":4}。請依 [stabilizer, identity, contains_identity, product_closed, inverse_closed, subgroup, certificate] 欄序回答。
查看答案與解釋
([0, 1, 2], 0, 是, 是, 是, 是, identity_product_inverse_closure)
Wave6第三層核對=([0, 1, 2], 0, 是, 是, 是, 是, identity_product_inverse_closure)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-subgroup-certificate · candidate
43. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-subgroup-certificate；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]],"point":3}。請依 [stabilizer, identity, contains_identity, product_closed, inverse_closed, subgroup, certificate] 欄序回答。
查看答案與解釋
([0], 0, 是, 是, 是, 是, identity_product_inverse_closure)
Wave6第三層核對=([0], 0, 是, 是, 是, 是, identity_product_inverse_closure)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-subgroup-certificate · candidate
44. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-subgroup-certificate；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]],"point":2}。請依 [stabilizer, identity, contains_identity, product_closed, inverse_closed, subgroup, certificate] 欄序回答。
查看答案與解釋
([0], 0, 是, 是, 是, 是, identity_product_inverse_closure)
Wave6第三層核對=([0], 0, 是, 是, 是, 是, identity_product_inverse_closure)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-subgroup-certificate · candidate
45. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-subgroup-certificate；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]],"point":1}。請依 [stabilizer, identity, contains_identity, product_closed, inverse_closed, subgroup, certificate] 欄序回答。
查看答案與解釋
([0], 0, 是, 是, 是, 是, identity_product_inverse_closure)
Wave6第三層核對=([0], 0, 是, 是, 是, 是, identity_product_inverse_closure)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-subgroup-certificate · candidate
46. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-subgroup-certificate；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]],"point":2}。請依 [stabilizer, identity, contains_identity, product_closed, inverse_closed, subgroup, certificate] 欄序回答。
查看答案與解釋
([0, 1], 0, 是, 是, 是, 是, identity_product_inverse_closure)
Wave6第三層核對=([0, 1], 0, 是, 是, 是, 是, identity_product_inverse_closure)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-subgroup-certificate · candidate
47. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-subgroup-certificate；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]],"point":0}。請依 [stabilizer, identity, contains_identity, product_closed, inverse_closed, subgroup, certificate] 欄序回答。
查看答案與解釋
([0], 0, 是, 是, 是, 是, identity_product_inverse_closure)
Wave6第三層核對=([0], 0, 是, 是, 是, 是, identity_product_inverse_closure)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-subgroup-certificate · candidate
48. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-subgroup-certificate；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]],"point":6}。請依 [stabilizer, identity, contains_identity, product_closed, inverse_closed, subgroup, certificate] 欄序回答。
查看答案與解釋
([0, 1, 2, 3], 0, 是, 是, 是, 是, identity_product_inverse_closure)
Wave6第三層核對=([0, 1, 2, 3], 0, 是, 是, 是, 是, identity_product_inverse_closure)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-subgroup-certificate · candidate
49. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-subgroup-certificate；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]],"point":5}。請依 [stabilizer, identity, contains_identity, product_closed, inverse_closed, subgroup, certificate] 欄序回答。
查看答案與解釋
([0, 1, 2, 3, 4], 0, 是, 是, 是, 是, identity_product_inverse_closure)
Wave6第三層核對=([0, 1, 2, 3, 4], 0, 是, 是, 是, 是, identity_product_inverse_closure)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-subgroup-certificate · candidate
50. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-subgroup-certificate；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]],"point":4}。請依 [stabilizer, identity, contains_identity, product_closed, inverse_closed, subgroup, certificate] 欄序回答。
查看答案與解釋
([0], 0, 是, 是, 是, 是, identity_product_inverse_closure)
Wave6第三層核對=([0], 0, 是, 是, 是, 是, identity_product_inverse_closure)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-subgroup-certificate · candidate
51. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-membership-audit；資料={"group_table":[[0,1],[1,0]],"identity":0,"point_count":2,"action_table":[[0,1],[1,0]],"point":0,"group_element":0}。請依 [group_element, point, image, fixes_point, in_stabilizer] 欄序回答。
查看答案與解釋
(0, 0, 0, 是, 是)
Wave6第三層核對=(0, 0, 0, 是, 是)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-membership-audit · candidate
52. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-membership-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]],"point":1,"group_element":1}。請依 [group_element, point, image, fixes_point, in_stabilizer] 欄序回答。
查看答案與解釋
(1, 1, 2, 否, 否)
Wave6第三層核對=(1, 1, 2, 否, 否)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-membership-audit · candidate
53. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-membership-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]],"point":2,"group_element":2}。請依 [group_element, point, image, fixes_point, in_stabilizer] 欄序回答。
查看答案與解釋
(2, 2, 0, 否, 否)
Wave6第三層核對=(2, 2, 0, 否, 否)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-membership-audit · candidate
54. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-membership-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]],"point":3,"group_element":3}。請依 [group_element, point, image, fixes_point, in_stabilizer] 欄序回答。
查看答案與解釋
(3, 3, 1, 否, 否)
Wave6第三層核對=(3, 3, 1, 否, 否)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-membership-audit · candidate
55. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-membership-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]],"point":4,"group_element":4}。請依 [group_element, point, image, fixes_point, in_stabilizer] 欄序回答。
查看答案與解釋
(4, 4, 2, 否, 否)
Wave6第三層核對=(4, 4, 2, 否, 否)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-membership-audit · candidate
56. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-membership-audit；資料={"group_table":[[0,1],[1,0]],"identity":0,"point_count":3,"action_table":[[0,1,2],[1,0,2]],"point":2,"group_element":1}。請依 [group_element, point, image, fixes_point, in_stabilizer] 欄序回答。
查看答案與解釋
(1, 2, 2, 是, 是)
Wave6第三層核對=(1, 2, 2, 是, 是)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-membership-audit · candidate
57. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-membership-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]],"point":2,"group_element":0}。請依 [group_element, point, image, fixes_point, in_stabilizer] 欄序回答。
查看答案與解釋
(0, 2, 2, 是, 是)
Wave6第三層核對=(0, 2, 2, 是, 是)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-membership-audit · candidate
58. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-membership-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]],"point":2,"group_element":3}。請依 [group_element, point, image, fixes_point, in_stabilizer] 欄序回答。
查看答案與解釋
(3, 2, 1, 否, 否)
Wave6第三層核對=(3, 2, 1, 否, 否)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-membership-audit · candidate
59. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-membership-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]],"point":2,"group_element":3}。請依 [group_element, point, image, fixes_point, in_stabilizer] 欄序回答。
查看答案與解釋
(3, 2, 0, 否, 否)
Wave6第三層核對=(3, 2, 0, 否, 否)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-membership-audit · candidate
60. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-membership-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]],"point":2,"group_element":3}。請依 [group_element, point, image, fixes_point, in_stabilizer] 欄序回答。
查看答案與解釋
(3, 2, 5, 否, 否)
Wave6第三層核對=(3, 2, 5, 否, 否)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-membership-audit · candidate
61. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-membership-audit；資料={"group_table":[[0,1],[1,0]],"identity":0,"point_count":4,"action_table":[[0,1,2,3],[1,0,2,3]],"point":2,"group_element":0}。請依 [group_element, point, image, fixes_point, in_stabilizer] 欄序回答。
查看答案與解釋
(0, 2, 2, 是, 是)
Wave6第三層核對=(0, 2, 2, 是, 是)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-membership-audit · candidate
62. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-membership-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]],"point":1,"group_element":2}。請依 [group_element, point, image, fixes_point, in_stabilizer] 欄序回答。
查看答案與解釋
(2, 1, 0, 否, 否)
Wave6第三層核對=(2, 1, 0, 否, 否)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-membership-audit · candidate
63. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-membership-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]],"point":0,"group_element":0}。請依 [group_element, point, image, fixes_point, in_stabilizer] 欄序回答。
查看答案與解釋
(0, 0, 0, 是, 是)
Wave6第三層核對=(0, 0, 0, 是, 是)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-membership-audit · candidate
64. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-membership-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]],"point":6,"group_element":3}。請依 [group_element, point, image, fixes_point, in_stabilizer] 欄序回答。
查看答案與解釋
(3, 6, 6, 是, 是)
Wave6第三層核對=(3, 6, 6, 是, 是)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-membership-audit · candidate
65. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-membership-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]],"point":6,"group_element":2}。請依 [group_element, point, image, fixes_point, in_stabilizer] 欄序回答。
查看答案與解釋
(2, 6, 6, 是, 是)
Wave6第三層核對=(2, 6, 6, 是, 是)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-membership-audit · candidate
66. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-membership-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]],"point":0,"group_element":1}。請依 [group_element, point, image, fixes_point, in_stabilizer] 欄序回答。
查看答案與解釋
(1, 0, 1, 否, 否)
Wave6第三層核對=(1, 0, 1, 否, 否)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-membership-audit · candidate
67. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-membership-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]],"point":4,"group_element":1}。請依 [group_element, point, image, fixes_point, in_stabilizer] 欄序回答。
查看答案與解釋
(1, 4, 4, 是, 是)
Wave6第三層核對=(1, 4, 4, 是, 是)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-membership-audit · candidate
68. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-membership-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]],"point":3,"group_element":1}。請依 [group_element, point, image, fixes_point, in_stabilizer] 欄序回答。
查看答案與解釋
(1, 3, 0, 否, 否)
Wave6第三層核對=(1, 3, 0, 否, 否)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-membership-audit · candidate
69. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-membership-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]],"point":2,"group_element":3}。請依 [group_element, point, image, fixes_point, in_stabilizer] 欄序回答。
查看答案與解釋
(3, 2, 0, 否, 否)
Wave6第三層核對=(3, 2, 0, 否, 否)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-membership-audit · candidate
70. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-membership-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]],"point":1,"group_element":1}。請依 [group_element, point, image, fixes_point, in_stabilizer] 欄序回答。
查看答案與解釋
(1, 1, 2, 否, 否)
Wave6第三層核對=(1, 1, 2, 否, 否)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-membership-audit · candidate
71. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-membership-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]],"point":2,"group_element":0}。請依 [group_element, point, image, fixes_point, in_stabilizer] 欄序回答。
查看答案與解釋
(0, 2, 2, 是, 是)
Wave6第三層核對=(0, 2, 2, 是, 是)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-membership-audit · candidate
72. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-membership-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]],"point":0,"group_element":0}。請依 [group_element, point, image, fixes_point, in_stabilizer] 欄序回答。
查看答案與解釋
(0, 0, 0, 是, 是)
Wave6第三層核對=(0, 0, 0, 是, 是)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-membership-audit · candidate
73. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-membership-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]],"point":6,"group_element":2}。請依 [group_element, point, image, fixes_point, in_stabilizer] 欄序回答。
查看答案與解釋
(2, 6, 6, 是, 是)
Wave6第三層核對=(2, 6, 6, 是, 是)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-membership-audit · candidate
74. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-membership-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]],"point":5,"group_element":3}。請依 [group_element, point, image, fixes_point, in_stabilizer] 欄序回答。
查看答案與解釋
(3, 5, 5, 是, 是)
Wave6第三層核對=(3, 5, 5, 是, 是)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-membership-audit · candidate
75. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-membership-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]],"point":4,"group_element":0}。請依 [group_element, point, image, fixes_point, in_stabilizer] 欄序回答。
查看答案與解釋
(0, 4, 4, 是, 是)
Wave6第三層核對=(0, 4, 4, 是, 是)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-membership-audit · candidate
76. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-point-boundary；資料={"group_table":[[0,1],[1,0]],"identity":0,"point_count":2,"action_table":[[0,1],[1,0]],"point":0,"other_point":1}。請依 [point, stabilizer, other_point, other_stabilizer, same_stabilizer, orbit_or_kernel_identification_claim, boundary] 欄序回答。
固定的否是不把stabilizer、orbit與action kernel當成同一概念；不否定前面的same_stabilizer，也不宣稱特例不可能有集合相等。
查看答案與解釋
(0, [0], 1, [0], 是, 否, stabilizer_not_orbit_or_action_kernel)
Wave6第三層核對=(0, [0], 1, [0], 是, 否, stabilizer_not_orbit_or_action_kernel)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-point-boundary · candidate
77. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-point-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]],"point":1,"other_point":2}。請依 [point, stabilizer, other_point, other_stabilizer, same_stabilizer, orbit_or_kernel_identification_claim, boundary] 欄序回答。
固定的否是不把stabilizer、orbit與action kernel當成同一概念；不否定前面的same_stabilizer，也不宣稱特例不可能有集合相等。
查看答案與解釋
(1, [0], 2, [0], 是, 否, stabilizer_not_orbit_or_action_kernel)
Wave6第三層核對=(1, [0], 2, [0], 是, 否, stabilizer_not_orbit_or_action_kernel)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-point-boundary · candidate
78. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-point-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]],"point":2,"other_point":3}。請依 [point, stabilizer, other_point, other_stabilizer, same_stabilizer, orbit_or_kernel_identification_claim, boundary] 欄序回答。
固定的否是不把stabilizer、orbit與action kernel當成同一概念；不否定前面的same_stabilizer，也不宣稱特例不可能有集合相等。
查看答案與解釋
(2, [0], 3, [0], 是, 否, stabilizer_not_orbit_or_action_kernel)
Wave6第三層核對=(2, [0], 3, [0], 是, 否, stabilizer_not_orbit_or_action_kernel)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-point-boundary · candidate
79. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-point-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]],"point":3,"other_point":4}。請依 [point, stabilizer, other_point, other_stabilizer, same_stabilizer, orbit_or_kernel_identification_claim, boundary] 欄序回答。
固定的否是不把stabilizer、orbit與action kernel當成同一概念；不否定前面的same_stabilizer，也不宣稱特例不可能有集合相等。
查看答案與解釋
(3, [0], 4, [0], 是, 否, stabilizer_not_orbit_or_action_kernel)
Wave6第三層核對=(3, [0], 4, [0], 是, 否, stabilizer_not_orbit_or_action_kernel)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-point-boundary · candidate
80. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-point-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]],"point":4,"other_point":5}。請依 [point, stabilizer, other_point, other_stabilizer, same_stabilizer, orbit_or_kernel_identification_claim, boundary] 欄序回答。
固定的否是不把stabilizer、orbit與action kernel當成同一概念；不否定前面的same_stabilizer，也不宣稱特例不可能有集合相等。
查看答案與解釋
(4, [0], 5, [0], 是, 否, stabilizer_not_orbit_or_action_kernel)
Wave6第三層核對=(4, [0], 5, [0], 是, 否, stabilizer_not_orbit_or_action_kernel)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-point-boundary · candidate
81. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-point-boundary；資料={"group_table":[[0,1],[1,0]],"identity":0,"point_count":3,"action_table":[[0,1,2],[1,0,2]],"point":2,"other_point":0}。請依 [point, stabilizer, other_point, other_stabilizer, same_stabilizer, orbit_or_kernel_identification_claim, boundary] 欄序回答。
固定的否是不把stabilizer、orbit與action kernel當成同一概念；不否定前面的same_stabilizer，也不宣稱特例不可能有集合相等。
查看答案與解釋
(2, [0, 1], 0, [0], 否, 否, stabilizer_not_orbit_or_action_kernel)
Wave6第三層核對=(2, [0, 1], 0, [0], 否, 否, stabilizer_not_orbit_or_action_kernel)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-point-boundary · candidate
82. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-point-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]],"point":2,"other_point":3}。請依 [point, stabilizer, other_point, other_stabilizer, same_stabilizer, orbit_or_kernel_identification_claim, boundary] 欄序回答。
固定的否是不把stabilizer、orbit與action kernel當成同一概念；不否定前面的same_stabilizer，也不宣稱特例不可能有集合相等。
查看答案與解釋
(2, [0], 3, [0, 1, 2], 否, 否, stabilizer_not_orbit_or_action_kernel)
Wave6第三層核對=(2, [0], 3, [0, 1, 2], 否, 否, stabilizer_not_orbit_or_action_kernel)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-point-boundary · candidate
83. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-point-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]],"point":2,"other_point":3}。請依 [point, stabilizer, other_point, other_stabilizer, same_stabilizer, orbit_or_kernel_identification_claim, boundary] 欄序回答。
固定的否是不把stabilizer、orbit與action kernel當成同一概念；不否定前面的same_stabilizer，也不宣稱特例不可能有集合相等。
查看答案與解釋
(2, [0], 3, [0], 是, 否, stabilizer_not_orbit_or_action_kernel)
Wave6第三層核對=(2, [0], 3, [0], 是, 否, stabilizer_not_orbit_or_action_kernel)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-point-boundary · candidate
84. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-point-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]],"point":2,"other_point":3}。請依 [point, stabilizer, other_point, other_stabilizer, same_stabilizer, orbit_or_kernel_identification_claim, boundary] 欄序回答。
固定的否是不把stabilizer、orbit與action kernel當成同一概念；不否定前面的same_stabilizer，也不宣稱特例不可能有集合相等。
查看答案與解釋
(2, [0], 3, [0], 是, 否, stabilizer_not_orbit_or_action_kernel)
Wave6第三層核對=(2, [0], 3, [0], 是, 否, stabilizer_not_orbit_or_action_kernel)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-point-boundary · candidate
85. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-point-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]],"point":2,"other_point":3}。請依 [point, stabilizer, other_point, other_stabilizer, same_stabilizer, orbit_or_kernel_identification_claim, boundary] 欄序回答。
固定的否是不把stabilizer、orbit與action kernel當成同一概念；不否定前面的same_stabilizer，也不宣稱特例不可能有集合相等。
查看答案與解釋
(2, [0], 3, [0], 是, 否, stabilizer_not_orbit_or_action_kernel)
Wave6第三層核對=(2, [0], 3, [0], 是, 否, stabilizer_not_orbit_or_action_kernel)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-point-boundary · candidate
86. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-point-boundary；資料={"group_table":[[0,1],[1,0]],"identity":0,"point_count":4,"action_table":[[0,1,2,3],[1,0,2,3]],"point":2,"other_point":3}。請依 [point, stabilizer, other_point, other_stabilizer, same_stabilizer, orbit_or_kernel_identification_claim, boundary] 欄序回答。
固定的否是不把stabilizer、orbit與action kernel當成同一概念；不否定前面的same_stabilizer，也不宣稱特例不可能有集合相等。
查看答案與解釋
(2, [0, 1], 3, [0, 1], 是, 否, stabilizer_not_orbit_or_action_kernel)
Wave6第三層核對=(2, [0, 1], 3, [0, 1], 是, 否, stabilizer_not_orbit_or_action_kernel)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-point-boundary · candidate
87. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-point-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]],"point":1,"other_point":2}。請依 [point, stabilizer, other_point, other_stabilizer, same_stabilizer, orbit_or_kernel_identification_claim, boundary] 欄序回答。
固定的否是不把stabilizer、orbit與action kernel當成同一概念；不否定前面的same_stabilizer，也不宣稱特例不可能有集合相等。
查看答案與解釋
(1, [0], 2, [0], 是, 否, stabilizer_not_orbit_or_action_kernel)
Wave6第三層核對=(1, [0], 2, [0], 是, 否, stabilizer_not_orbit_or_action_kernel)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-point-boundary · candidate
88. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-point-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]],"point":0,"other_point":1}。請依 [point, stabilizer, other_point, other_stabilizer, same_stabilizer, orbit_or_kernel_identification_claim, boundary] 欄序回答。
固定的否是不把stabilizer、orbit與action kernel當成同一概念；不否定前面的same_stabilizer，也不宣稱特例不可能有集合相等。
查看答案與解釋
(0, [0], 1, [0], 是, 否, stabilizer_not_orbit_or_action_kernel)
Wave6第三層核對=(0, [0], 1, [0], 是, 否, stabilizer_not_orbit_or_action_kernel)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-point-boundary · candidate
89. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-point-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]],"point":6,"other_point":0}。請依 [point, stabilizer, other_point, other_stabilizer, same_stabilizer, orbit_or_kernel_identification_claim, boundary] 欄序回答。
固定的否是不把stabilizer、orbit與action kernel當成同一概念；不否定前面的same_stabilizer，也不宣稱特例不可能有集合相等。
查看答案與解釋
(6, [0, 1, 2, 3, 4], 0, [0], 否, 否, stabilizer_not_orbit_or_action_kernel)
Wave6第三層核對=(6, [0, 1, 2, 3, 4], 0, [0], 否, 否, stabilizer_not_orbit_or_action_kernel)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-point-boundary · candidate
90. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-point-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]],"point":6,"other_point":7}。請依 [point, stabilizer, other_point, other_stabilizer, same_stabilizer, orbit_or_kernel_identification_claim, boundary] 欄序回答。
固定的否是不把stabilizer、orbit與action kernel當成同一概念；不否定前面的same_stabilizer，也不宣稱特例不可能有集合相等。
查看答案與解釋
(6, [0, 1, 2, 3, 4, 5], 7, [0, 1, 2, 3, 4, 5], 是, 否, stabilizer_not_orbit_or_action_kernel)
Wave6第三層核對=(6, [0, 1, 2, 3, 4, 5], 7, [0, 1, 2, 3, 4, 5], 是, 否, stabilizer_not_orbit_or_action_kernel)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-point-boundary · candidate
91. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-point-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]],"point":0,"other_point":1}。請依 [point, stabilizer, other_point, other_stabilizer, same_stabilizer, orbit_or_kernel_identification_claim, boundary] 欄序回答。
固定的否是不把stabilizer、orbit與action kernel當成同一概念；不否定前面的same_stabilizer，也不宣稱特例不可能有集合相等。
查看答案與解釋
(0, [0], 1, [0], 是, 否, stabilizer_not_orbit_or_action_kernel)
Wave6第三層核對=(0, [0], 1, [0], 是, 否, stabilizer_not_orbit_or_action_kernel)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-point-boundary · candidate
92. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-point-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]],"point":4,"other_point":5}。請依 [point, stabilizer, other_point, other_stabilizer, same_stabilizer, orbit_or_kernel_identification_claim, boundary] 欄序回答。
固定的否是不把stabilizer、orbit與action kernel當成同一概念；不否定前面的same_stabilizer，也不宣稱特例不可能有集合相等。
查看答案與解釋
(4, [0, 1, 2], 5, [0, 1, 2], 是, 否, stabilizer_not_orbit_or_action_kernel)
Wave6第三層核對=(4, [0, 1, 2], 5, [0, 1, 2], 是, 否, stabilizer_not_orbit_or_action_kernel)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-point-boundary · candidate
93. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-point-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]],"point":3,"other_point":4}。請依 [point, stabilizer, other_point, other_stabilizer, same_stabilizer, orbit_or_kernel_identification_claim, boundary] 欄序回答。
固定的否是不把stabilizer、orbit與action kernel當成同一概念；不否定前面的same_stabilizer，也不宣稱特例不可能有集合相等。
查看答案與解釋
(3, [0], 4, [0, 1, 2, 3], 否, 否, stabilizer_not_orbit_or_action_kernel)
Wave6第三層核對=(3, [0], 4, [0, 1, 2, 3], 否, 否, stabilizer_not_orbit_or_action_kernel)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-point-boundary · candidate
94. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-point-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]],"point":2,"other_point":3}。請依 [point, stabilizer, other_point, other_stabilizer, same_stabilizer, orbit_or_kernel_identification_claim, boundary] 欄序回答。
固定的否是不把stabilizer、orbit與action kernel當成同一概念；不否定前面的same_stabilizer，也不宣稱特例不可能有集合相等。
查看答案與解釋
(2, [0], 3, [0], 是, 否, stabilizer_not_orbit_or_action_kernel)
Wave6第三層核對=(2, [0], 3, [0], 是, 否, stabilizer_not_orbit_or_action_kernel)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-point-boundary · candidate
95. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-point-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]],"point":1,"other_point":2}。請依 [point, stabilizer, other_point, other_stabilizer, same_stabilizer, orbit_or_kernel_identification_claim, boundary] 欄序回答。
固定的否是不把stabilizer、orbit與action kernel當成同一概念；不否定前面的same_stabilizer，也不宣稱特例不可能有集合相等。
查看答案與解釋
(1, [0], 2, [0], 是, 否, stabilizer_not_orbit_or_action_kernel)
Wave6第三層核對=(1, [0], 2, [0], 是, 否, stabilizer_not_orbit_or_action_kernel)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-point-boundary · candidate
96. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-point-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]],"point":2,"other_point":3}。請依 [point, stabilizer, other_point, other_stabilizer, same_stabilizer, orbit_or_kernel_identification_claim, boundary] 欄序回答。
固定的否是不把stabilizer、orbit與action kernel當成同一概念；不否定前面的same_stabilizer，也不宣稱特例不可能有集合相等。
查看答案與解釋
(2, [0, 1], 3, [0, 1], 是, 否, stabilizer_not_orbit_or_action_kernel)
Wave6第三層核對=(2, [0, 1], 3, [0, 1], 是, 否, stabilizer_not_orbit_or_action_kernel)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-point-boundary · candidate
97. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-point-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]],"point":0,"other_point":1}。請依 [point, stabilizer, other_point, other_stabilizer, same_stabilizer, orbit_or_kernel_identification_claim, boundary] 欄序回答。
固定的否是不把stabilizer、orbit與action kernel當成同一概念；不否定前面的same_stabilizer，也不宣稱特例不可能有集合相等。
查看答案與解釋
(0, [0], 1, [0], 是, 否, stabilizer_not_orbit_or_action_kernel)
Wave6第三層核對=(0, [0], 1, [0], 是, 否, stabilizer_not_orbit_or_action_kernel)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-point-boundary · candidate
98. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-point-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]],"point":6,"other_point":7}。請依 [point, stabilizer, other_point, other_stabilizer, same_stabilizer, orbit_or_kernel_identification_claim, boundary] 欄序回答。
固定的否是不把stabilizer、orbit與action kernel當成同一概念；不否定前面的same_stabilizer，也不宣稱特例不可能有集合相等。
查看答案與解釋
(6, [0, 1, 2, 3], 7, [0, 1, 2, 3], 是, 否, stabilizer_not_orbit_or_action_kernel)
Wave6第三層核對=(6, [0, 1, 2, 3], 7, [0, 1, 2, 3], 是, 否, stabilizer_not_orbit_or_action_kernel)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-point-boundary · candidate
99. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-point-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]],"point":5,"other_point":6}。請依 [point, stabilizer, other_point, other_stabilizer, same_stabilizer, orbit_or_kernel_identification_claim, boundary] 欄序回答。
固定的否是不把stabilizer、orbit與action kernel當成同一概念；不否定前面的same_stabilizer，也不宣稱特例不可能有集合相等。
查看答案與解釋
(5, [0, 1, 2, 3, 4], 6, [0, 1, 2, 3, 4], 是, 否, stabilizer_not_orbit_or_action_kernel)
Wave6第三層核對=(5, [0, 1, 2, 3, 4], 6, [0, 1, 2, 3, 4], 是, 否, stabilizer_not_orbit_or_action_kernel)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-point-boundary · candidate
100. 有限群作用的穩定子群
完整已認證有限群作用與指定point。操作=stabilizer-point-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]],"point":4,"other_point":5}。請依 [point, stabilizer, other_point, other_stabilizer, same_stabilizer, orbit_or_kernel_identification_claim, boundary] 欄序回答。
固定的否是不把stabilizer、orbit與action kernel當成同一概念；不否定前面的same_stabilizer，也不宣稱特例不可能有集合相等。
查看答案與解釋
(4, [0], 5, [0], 是, 否, stabilizer_not_orbit_or_action_kernel)
Wave6第三層核對=(4, [0], 5, [0], 是, 否, stabilizer_not_orbit_or_action_kernel)；依完整明示資料獨立重算；stabilizer遍歷全部g並完整驗identity、product與inverse closure；不得把single fixed element、action kernel或orbit混同stabilizer。
本題逐步詳解（AI 二次覆核）
有限群作用的穩定子群 · qf-mod40-stabilizer-point-boundary · candidate
原始題目 JSONL · 驗收報告