| 某些弱拟正规子群对有限群可解性的影响 |
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| 引用本文： | 陈顺民,陈贵云.某些弱拟正规子群对有限群可解性的影响[J].四川大学学报(自然科学版),2007,44(3):472-476. |
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| 作者姓名： | 陈顺民 陈贵云 |
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| 作者单位： | 1. 陕西师范大学数学与信息科学学院,西安,710062;重庆文理学院数学与计算机科学系,重庆,402160
2. 西南大学数学与统计学院,重庆,400715 |
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| 基金项目： | 国家自然科学基金;重庆市科委自然科学基金 |
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| 摘 要： | 利用弱拟正规子群及S弱拟正规子群，得到了有限群的可解性的一些新刻画.主要获得了下列结论：(i)若群G有两个不共轭的可解极大子群均在G中弱拟正规，则G可解；(ii)群G可解当且仅当G存在可解的极大子群在G中弱拟正规，且G与交错群A5、PSL2(7)及PSL3(3)无关.
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| 关 键 词： | 弱拟正规子群 极大子群 可解群 |
| 文章编号： | 0490-6756（2007）03-0472-05 |
| 修稿时间： | 2005-02-25 |
The influence of some weakly quasinormal subgroups on the solvability of finite groups |
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| CHEN Shun-min and CHEN Gui-yun.The influence of some weakly quasinormal subgroups on the solvability of finite groups[J].Journal of Sichuan University (Natural Science Edition),2007,44(3):472-476. |
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| Authors: | CHEN Shun-min and CHEN Gui-yun |
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| Institution: | School of Mathematics and Informations Science, Shanxi Normal University;Department of Mathematics and Computer Science, Chongqing University of Arts and Sciences,Department of Mathematics and Statistics, Sounthwest University |
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| Abstract: | The authors come to some new criteria of solvability of finite groups under the assumptions that the groups have some kinds of weakly quasinormal or S-weakly quasinormal subgroups.Some results are the following:(i) Let G be a finite group having two maximal subgroups that are solvable and not conjugate in G.If the maximal subgroups are weakly quasinormal in G,then G is solvable.(ii) Let G be a finite group.G is a solvable group if and only if G has a solvable maximal subgroup being weakly quasinormal in G and no section isomorphic to group A5,PSL2(7) and PSL3(3). |
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| Keywords: | weakly quasinormal subgroup maximal subgroup solvable group |
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