| 关于有限群子群的弱S-可补性 |
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| 引用本文： | 苏宁,李样明,王燕鸣.关于有限群子群的弱S-可补性[J].数学年刊A辑(中文版),2015,36(1):91-102. |
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| 作者姓名： | 苏宁 李样明 王燕鸣 |
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| 作者单位： | 中山大学数学与计算科学学院, 广州 510275.;广东第二师范学院数学系, 广州 510310.;中山大学岭南学院, 广州 510275. |
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| 基金项目： | 国家自然科学基金 (No.11401597, No.11171353, No.11271085), 广东省自然科学基金 (No.S2011010004447) 和广东省高校学科建设专项项目(No.2012KJCX0081) |
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| 摘 要： | 设G是一个有限群,H是G的一个子群.称H为G的一个s-置换子群,若对于G的任意Sylow子群P,成立HP=PH.称H为G的一个弱s-可补的子群.若存在G的一个子群T,使得G=HT且H∩T≤H_s G,其中H_s G是包含在H中的G的最大的s-置换子群.本文在假设G的某些子群是弱s-可补的前提下,得到了G的一个结构定理,并推广了许多近期的结果.
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| 关 键 词： | 弱s-可补子群 p-幂零群 u-超中心 p-可解群的p-长 |
The Weakly s-Supplemented Property of Finite Groups |
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| SU Ning,LI Yangming and WANG Yanming.The Weakly s-Supplemented Property of Finite Groups[J].Chinese Annals of Mathematics,2015,36(1):91-102. |
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| Authors: | SU Ning LI Yangming and WANG Yanming |
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| Institution: | School of Mathematics and Computational Science, Sun Yatsen University,
Guangzhou 510275, China.;Department of Mathematics, Guangdong University of
Education, Guangzhou 510310, China.;Lingnan College, Sun Yatsen University,
Guangzhou 510275, China. |
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| Abstract: | Suppose that G is a finite group and H is a subgroup of G. H is
said to be s-permutable in G if HP = PH for any Sylow
subgroup P of G. H is said to be weakly s-supplemented in
G if there is a subgroup T of G, such that
G=HT and H\cap T \leq H_{{\rm s}G}, where H_{{\rm s}G} is the biggest
s-permutable subgroup of G contained in H. In this paper, a
structural theorem of finite groups is given under the
hypothesis that some subgroups of G are weakly s-supplemented
subgroups of G. Many recent results are extended. |
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| Keywords: | Weakly s-supplemented subgroup p-Nilpotent group ${\cal U}$-Hypercenter p-Length of a
p-solvable group |
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