| 与Sylow-子群X-可置换的子群对有限群的影响 |
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| 引用本文： | 苏宁,王燕鸣.与Sylow-子群X-可置换的子群对有限群的影响[J].数学年刊A辑(中文版),2014,35(5):511-522. |
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| 作者姓名： | 苏宁 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.;中山大学数学与计算科学学院, 广州~510275. 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.11171353) 和中山大学青年教师起步资助计划 |
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| 摘 要： | 设X是有限群G中的一个非空子集,H和T是G的两个子群.称日与T在G中是X-可置换的,如果存在元素x∈X,满足HT~x=T~xH.作者探讨了当有限群G的某些子群与G的某些Sylow子群是X-可置换时G的结构.
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| 关 键 词： | 有限群 $X$-可置换性 $p$-超可解 |
The Influence of Subgroups X-Permutable with Sylow Subgroups |
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| SU Ning and WANG Yanming.The Influence of Subgroups X-Permutable with Sylow Subgroups[J].Chinese Annals of Mathematics,2014,35(5):511-522. |
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| Authors: | SU Ning and WANG Yanming |
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| Institution: | School of Mathematics and Computational Science, Sun Yatsen
University,
Guangzhou 510275, China.;School of Mathematics and Computational Science, Sun Yatsen
University,
Guangzhou 510275, China. Lingnan College, Sun Yatsen University,
Guangzhou 510275, China. |
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| Abstract: | Suppose that $X$ is a nonempty subset of a
finite group $G$ and let $H$ and $T$ be subgroups of $G$. $H$ is
said to be $X$-permutable with $T$ in $G$ if there is an element
$x\in X$ such that $HT^{x}=T^{x}H$. This paper studies the structure
of $G$ under the assumption that certain classes of subgroups of $G$
are $X$-permutable with some Sylow subgroups of $G$. |
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| Keywords: | Finite groups $X$-Permutable Supersoluble |
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