$SE$-Supplemented Subgroups of Finite Groups

Abstract

Let $G$ be a finite group, $H$ a subgroup of $G$ and $H_{seG}$ be the subgroup generated by all subgroups of $H$ which are $S$-quasinormally embedded in $G$. Then we say that $H$ is $SE$-supplemented in $G$ if $G$ has a subgroup $T$ such that $HT=G$ and $H\cap T\le H_{seG}$. We investigate the influence of $SE$-quasinormally embedded of some subgroups on the structure of finite groups. Our results improve and extend a series of recent results.