| 二次极大子群中2阶及4阶循环子群拟正规的有限群 |
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| 引用本文： | 李世荣.二次极大子群中2阶及4阶循环子群拟正规的有限群[J].数学学报,1994,37(3):317-323. |
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| 作者姓名： | 李世荣 |
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| 作者单位： | 广西大学数学系!南宁530004 |
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| 基金项目： | 国家自然科学基金资助课题． |
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| 摘 要： | 本文讨论２阶及４阶循环子群对群结构的影响．主要结果是下述定理：如果有限群Ｇ满足标题的条件，那么下列情形之一成立：（１）Ｇ有正规Ｓｙｌｏｗ ２－子群；（２） Ｇ为 ２－幂零；（３） Ｇ ≌ Ｓ４；（４） Ｇ＝ＰＱ，其中 Ｐ为阶 ２４广义四元数群， Ｑ为 ３阶循环群；（５） Ｇ ≌ Ａ５或 ＳＬ（２，５）．
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| 关 键 词： | 有限群 二次极大子群 极小子群 构造 |
| 收稿时间： | 1991-10-28 |
Finite Groups in Whose Second Maximal Subgroups the Cyclic Subgroups of Order 2 and 4 are Quasinarmal |
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| Li Shirong.Finite Groups in Whose Second Maximal Subgroups the Cyclic Subgroups of Order 2 and 4 are Quasinarmal[J].Acta Mathematica Sinica,1994,37(3):317-323. |
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| Authors: | Li Shirong |
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| Institution: | Li Shirong (Department of Mathematics, Guangxi University, Guangxi 530004, China) |
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| Abstract: | The purpose of this paper is to investigate the influence of subgroups of order 2 and 4 on the structure of finite groups. The main result is as follows: If a finite group G satisfies the condition in the tatle, then one of the following holds: (1) G possesses a normal Sylow 2- subgroup; (2) G is 2-nilpotent; (3) G ≌ S4; (4) G = PQ,where P is a generalized quaternion group of order 24 and Q is a cyclic group of order 3; (5) G ≌ A5 or SL(2, 5). |
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| Keywords: | finite group second maximal subgroup minimal subgroup structure |
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