# 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](https://ocme.evemisslab.com/data/i18n/question-output-protocols.json)



## 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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0001/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0002/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0003/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0004/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0005/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0006/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0007/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0008/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0009/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0010/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0011/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0012/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0013/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0014/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0015/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0016/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0017/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0018/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0019/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0020/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0021/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0022/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0023/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0024/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0025/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0026/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0027/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0028/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0029/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0030/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0031/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0032/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0033/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0034/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0035/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0036/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0037/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0038/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0039/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0040/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0041/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0042/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0043/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0044/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0045/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0046/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0047/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0048/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0049/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0050/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0051/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0052/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0053/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0054/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0055/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0056/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0057/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0058/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0059/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0060/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0061/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0062/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0063/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0064/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0065/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0066/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0067/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0068/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0069/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0070/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0071/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0072/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0073/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0074/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0075/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0076/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0077/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0078/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0079/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0080/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0081/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0082/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0083/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0084/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0085/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0086/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0087/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0088/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0089/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0090/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0091/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0092/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0093/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0094/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0095/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0096/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0097/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0098/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0099/)

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）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261109-r01-finite-group-stabilizer-0100/)

有限群作用的穩定子群 · qf-mod40-stabilizer-point-boundary · candidate



[原始題目 JSONL](https://ocme.evemisslab.com/data/questions/batches/batch-20261014-advance-20261109-r01-finite-group-stabilizer-foundations/questions.jsonl) · [驗收報告](https://ocme.evemisslab.com/data/questions/batches/batch-20261014-advance-20261109-r01-finite-group-stabilizer-foundations/validation-report.json)