| 所有非交换子群皆次正规的有限群 |
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| 引用本文： | 雒晓良,郭秀云.所有非交换子群皆次正规的有限群[J].上海大学学报(自然科学版),2009,15(1):11-13. |
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| 作者姓名： | 雒晓良 郭秀云 |
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| 作者单位： | 上海大学 理学院,上海 200444 |
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| 基金项目： | 国家自然科学基金，上海大学研究生创新基金 |
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| 摘 要： | 研究了每一非交换子群皆为次正规的有限非幂零群的结构.首先证明这类群为可解群， 其次通过分析Sylow子群的性质给出了这类群的一个充要条件以及一些结构性质，最后作为应用讨论具有上述性质的超可解群.
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| 关 键 词： | 次正规子群 A-群 非幂零群 超可解群 |
| 收稿时间： | 2007-06-11 |
Finite Groups with Every Non-abelian Subgroup Being Subnormal |
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| LUO Xiao-liang,GUO Xiu-yun.Finite Groups with Every Non-abelian Subgroup Being Subnormal[J].Journal of Shanghai University(Natural Science),2009,15(1):11-13. |
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| Authors: | LUO Xiao-liang GUO Xiu-yun |
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| Institution: | College of Sciences, Shanghai University, Shanghai 200444, China |
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| Abstract: | In this paper， the finite non-nilpotent group with every non-abelian subgroup being subnormal is investigated.It’s shown that such groups are solvable, and then give a necessary and sufficient condition and some structures for this kind of groups by taking into account the Sylow subgroups. As an application, the super solvable group with the above property is discussed. |
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| Keywords: | subnormal subgroup A-group non-nilpotent group super-solvable group |
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