The influence of ${\mathfrak{F}}_{\mathrm{s}}$-quasinormality of subgroups on the structure of finite groups

Abstract

Let $\mathfrak{F}$ 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 $\mathfrak{F}$-hypercenter $Z_{\infty }^{\mathfrak{F}}(G/H_G)$ of $G/H_G$. In this paper, we investigate further the influence of ${\mathfrak{F}}_{\mathrm{s}}$-quasinormality of some subgroups on the structure of finite groups. New characterization of some classes of finite groups are obtained.

arXiv commentThis is a revised version of the paper published in Publ. Math. Debrecen