陈顺民, 陈贵云. 共轭置换子群与有限群的可解性[J]. 云南大学学报(自然科学版), 2008, 30(5): 443-447.
引用本文: 陈顺民, 陈贵云. 共轭置换子群与有限群的可解性[J]. 云南大学学报(自然科学版), 2008, 30(5): 443-447.
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CHEN Shun-min, CHEN Gui-yun. Conjugate-permutable subgroups and the solvability of finite groups[J]. Journal of Yunnan University: Natural Sciences Edition, 2008, 30(5): 443-447.
Citation: CHEN Shun-min, CHEN Gui-yun. Conjugate-permutable subgroups and the solvability of finite groups[J]. Journal of Yunnan University: Natural Sciences Edition, 2008, 30(5): 443-447.
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共轭置换子群与有限群的可解性

Conjugate-permutable subgroups and the solvability of finite groups

    摘要
  • 摘要: 利用共轭置换子群的概念来研究有限群的可解性问题,获得了一个群为可解群的若干新刻画.特别,得到了:①若M·G,且M的极大子群均在G中共轭置换,则G可解;②设群G无截断PSL2(7),M·G,且|G:M|=pα,若M的2-极大子群均在G中共轭置换,则G可解.

     

    Abstract: The solvability of finite groups with some conjugate-permutable subgroups is investigated.Especially,the following results are obtained:① If M·G and the maximal subgroup of M are conjugate-permutable in G,then G is solvable.② Suppose that G is no section isomorphic to PSL2(7).If M·G with |G:M|=pα and the 2-maximal subgroups of M are conjugate-permutable in G,then G is solvable.

     

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