# On weakly <i>s</i> -normal subgroups of finite groups

### Abstract

Assume that $G$ is a finite group and $H$ is a subgroup of $G$. We say that $H$ is $s$-permutably imbedded in $G$ if, for every prime number p that divides $|H|$, a Sylow $p$-subgroup of $H$ is also a Sylow $p$-subgroup of some $s$-permutable subgroup of $G$; a subgroup $H$ is $s$-semipermutable in $G$ if $HG_p = G_pH$ for any Sylow $p$-subgroup $G_p$ of $G$ with $(p, |H|) = 1$; a subgroup $H$ is weakly $s$-normal in $G$ if there are a subnormal subgroup $T$ of $G$ and a subgroup $H_{*}$ of $H$ such that $G = HT$ and $H \bigcap T ≤ H_{*}$, where $H_{*}$ is a subgroup of $H$ that is either $s$-permutably imbedded or $s$-semipermutable in $G$. We investigate the influence of weakly $s$-normal subgroups on the structure of finite groups. Some recent results are generalized and unified.
Published

25.11.2011

How to Cite

*Ukrains’kyi Matematychnyi Zhurnal*, Vol. 63, no. 11, Nov. 2011, pp. 1555-64, https://umj.imath.kiev.ua/index.php/umj/article/view/2825.

Issue

Section

Research articles