| 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,2014,35(5):511~522 |
| 与Sylow-子群X-可置换的子群对有限群的影响 |
| The Influence of Subgroups X-Permutable with Sylow Subgroups |
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| DOI： |
| 中文关键词: 有限群, $X$-可置换性, $p$-超可解 |
| 英文关键词:Finite groups, $X$-Permutable, Supersoluble |
| 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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| 中文摘要: |
| 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$H$与$T$在$G$中是$X$-\可置换的, 如果存在元素$x\in X$,
满足$HT^{x}=T^{x}H$.
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. |
| 英文摘要: |
| 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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