2-极大子群的$F_s$-拟正规性

On $\mathfrak{F_{\mathrm s}}$-Quasinormality of 2-Maximal Subgroups

中文关键词:  $F_s$-拟正规子群  Sylow子群  极大子群  2-极大子群.

英文关键词:$\mathfrak{F_{\mathrm s}}$-quasinormal subgroup  Sylow subgroup  maximal subgroup  $2$-maximal subgroup.

中文摘要:

      $F$是一个群系. $G$的子群$H$在$G$中称为$F_s$-拟正规的,如果存在$G$的正规子群$T$,使得$HT$在$G$中是$s$-置换的并且$(H\cap T)H_G/H_G$包含在$G/H_G$的$F$超中心$Z^F_\infty(G/H_G)$中.本文利用$F_s$-拟正规子群研究了有限群的结构.获得了某些新的结果.

英文摘要:

      Let $\frak{F}$ be a class of finite groups. A subgroup $H$ of a finite group $G$ is said to be $\mathfrak{F_{\mathrm s}}$-quasinormal in $G$ if there exists a normal subgroup $T$ of $G$ such that $HT$ is $s$-permutable in $G$ and $(H\cap T)H_G/H_G$ is contained in the $\frak{F}$-hypercenter $Z_\infty ^\frak{F} (G/H_G)$ of $G/H_G$. In this paper, we use $\mathfrak{F_{\mathrm s}}$-quasinormal subgroups to study the structure of finite groups. Some new results are obtained.