| s-半置换子群对有限群的p-超可解性的影响 |
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| 引用本文： | 王丽芳.s-半置换子群对有限群的p-超可解性的影响[J].数学研究,2009,42(4):434-440. |
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| 作者姓名： | 王丽芳 |
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| 作者单位： | 山西师范大学数学与计算机科学学院,山西,临汾,041004 |
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| 基金项目： | 国家自然科学基金，效学天元基金，山西省回国留学人员基金，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资助 |
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| 摘 要： | 群G的子群H称为半置换的，若对任意的K≤G，只要（｜H｜，｜K｜）=1，就有HK=KH．H称为s-半置换的，若对任意的p｜｜G｜，只要（p，｜H｜）=1，就有PH=HP,其中P∈Sylp（G）．本文研究Sylow子群的极大子群及极小子群的s-半置换性对有限群的p-超可解性的影响．
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| 关 键 词： | s-半置换子群 极大子群 极小子群 p-超可解群 |
The Influence of s-semipermutable Subgroups on the p-supersolvability of Finite Groups |
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| Wang Lifang.The Influence of s-semipermutable Subgroups on the p-supersolvability of Finite Groups[J].Journal of Mathematical Study,2009,42(4):434-440. |
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| Authors: | Wang Lifang |
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| Institution: | Wang Lifang (School of Mathematics and Computer Science, Shanxi Normal University, Linfen, Shanxi 041004) |
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| Abstract: | Let G be a finite group. A subgroup H of a group G is called semipermutable if it is permutable with every subgroup K of G with (|H|,|K|)=1,and s-semipermutable if it is permutable with every Sylow p-subgroup of G with (p,(|H|))=1.The influence of s-semipermutablity of maximal subgroups and minimal subgroups of Sylow subgroup of a finite group on its p-supersolvability are investigated. |
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| Keywords: | s-semipermutable subgroups maximal subgroups minimal subgroups p-supersolvablegroups |
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