## Changwen Li

*On weakly $s$-permutably embedded subgroups*

Comment.Math.Univ.Carolin. 52,1 (2011) 21-29.**Abstract:**Suppose $G$ is a finite group and $H$ is a subgroup of $G$. $H$ is said to be $s$-permutably embedded in $G$ if for each prime $p$ dividing $|H|$, a Sylow $p$-subgroup of $H$ is also a Sylow $p$-subgroup of some $s$-permutable subgroup of $G$; $H$ is called weakly $s$-permutably embedded in $G$ if there are a subnormal subgroup $T$ of $G$ and an $s$-permutably embedded subgroup $H_{se}$ of $G$ contained in $H$ such that $G=HT$ and $H\cap T\leq H_{se}$. We investigate the influence of weakly $s$-permutably embedded subgroups on the $p$-nilpotency and $p$-supersolvability of finite groups.

**Keywords:** weakly $s$-permutably embedded subgroups, $p$-nilpotent, $n$-maximal subgroup

**AMS Subject Classification:** 20D10 20D20

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