| 弱-可补子群对有限群结构的影响 |
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| 引用本文： | 李先崇,黎先华.弱-可补子群对有限群结构的影响[J].广西师范大学学报(自然科学版),2012(1):25-28. |
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| 作者姓名： | 李先崇 黎先华 |
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| 作者单位： | 贵州师范大学数学与计算机科学学院;苏州大学数学科学学院 |
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| 基金项目： | 国家自然科学基金资助项目(11171243,10871032);江苏省自然科学基金资助项目(BK2008156) |
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| 摘 要： | 设H是G的子群,称H为弱-可补的,如果存在G的子群T使得G=HT且H∩T≤H-sG,其中H-sG是由H的所有在G中s-半置换子群生成的群。本文讨论有限群G的极小子群及4阶循环子群的弱-可补性对有限群结构的影响,给出了群G的p-幂零性的几个充分条件。
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| 关 键 词： | 弱-可补 p-幂零群 极小子群 |
Influence of Weakly -supplemented Subgroups on the Structure of Finite Groups |
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| LI Xian-chong,LI Xian-hua.Influence of Weakly -supplemented Subgroups on the Structure of Finite Groups[J].Journal of Guangxi Normal University(Natural Science Edition),2012(1):25-28. |
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| Authors: | LI Xian-chong LI Xian-hua |
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| Institution: | 1.School of Mathematics and Computer Science,Guizhou Normal University,Guiyang Guizhou 550001,China;2.School of Mathematical Science,Soochow University,Suzhou Jiangsu 215006,China) |
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| Abstract: | Let H be a subgroup of a finite group G.H is called weakly -supplemented if there exists asubgroup T of G such that G=TH and H∩T≤H-sG,where H-sG is the subgroup generalized by allsubgroups of H which are s-semipermutable in G.In this paper,the influence of minimal subgroups andsubgroups of order 4 which are weakly -supplemented in G on the structure of finite groups is studied,and several sufficient conditions of p-nilpotency of G are given. |
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| Keywords: | weakly -supplemented subgroups p-nilpotent group minimal subgroup |
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