| 弱s-拟正规子群对有限群的p-幂零性的影响 |
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| 引用本文： | 王丽芳,张慧芳.弱s-拟正规子群对有限群的p-幂零性的影响[J].纯粹数学与应用数学,2011,27(1):19-26. |
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| 作者姓名： | 王丽芳 张慧芳 |
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| 作者单位： | 山西师范大学数计学院,山西,临汾,041004 |
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| 基金项目： | 数学天元基金，山西省青年基金，山西省高等学校优秀青年学术带头人支持计划 |
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| 摘 要： | 群G的子群H称为G的弱s-拟正规子群,若G有次正规子群T,使得G=HT且H ∩T≤HsG,其中HsG是包含在H中的G的最大的s-拟正规子群.本文利用Sylow p-子群的极大子群的弱s-拟正规性得到有限群为p-幂零群的一些充分条件,并给出Schur-Zassenhaus定理的一种推广.
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| 关 键 词： | 弱s-拟正规子群 p-幂零群 Schur-Zassenhaus定理 |
The influence of weakly s-permutable subgroups on the p-nilpotency of finite groups |
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| WANG Li-fang,ZHANG Hui-fang.The influence of weakly s-permutable subgroups on the p-nilpotency of finite groups[J].Pure and Applied Mathematics,2011,27(1):19-26. |
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| Authors: | WANG Li-fang ZHANG Hui-fang |
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| Institution: | (School of Mathematics and Computer Science, Shanxi Normal University, Linfen 041004, China ) |
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| Abstract: | Let G be a finite group. A subgroup H of G is called weakly s-permutable in G if G has asubnormal subgroup T such that G = HT and T ∩ H ≤ HsG, where HsG is the largest s-quasinormal subgroupof G contained in H. The influence of weakly s-permutablity of maximal subgroups of Sylow subgroup of a finitegroup on its p-nilpotency are investigated. A generalization of Schur-Zassenhaus theorem is given in the paper. |
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| Keywords: | weakly s-permutable subgroups p-nilpotent groups Schur-Zassenhaus theorem |
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