X-s-置换子群

X-s-Permutable Subgroups

中文关键词:  有限群  群系  $X$-$s$-置换子群  Sylow子群  极大子群.

英文关键词:finite groups  formations  $X$-$s$-permutable subgroups  Sylow subgroups  maximal subgroups.

中文摘要:

      设$X$是群$G$的一个非空子集.子群$H$在$G$中称为是$X$-$s$-置换的,如果对于$G$的每个Sylow子群$T$,存在一个元素$x\in X$,使得$HT^{x}=T^{x}H$.本文中,我们得到有关$X$-$s$-置换子群的一些结果,并利用它们刻画了一些有限群的结构.

英文摘要:

      Let $X$ be a nonempty subset of a group $G$. A subgroup $H$ of $G$ is said to be $X$-$s$-permutable in $G$ if, for every Sylow subgroup $T$ of $G$, there exists an element $x\in X$ such that $HT^{x}=T^{x}H$. In this paper, we obtain some results about the $X$-$s$-permutable subgroups and use them to determine the structure of some finite groups.