Geodesic
On weakly $s$-permutably embedded subgroups
Commentationes Mathematicae Universitatis Carolinae, Tome 52 (2011) no. 1, pp. 21-29

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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.
Classification : 20D10, 20D20
Keywords: weakly $s$-permutably embedded subgroups; $p$-nilpotent; $n$-maximal subgroup 
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Li, Changwen. On weakly $s$-permutably embedded subgroups. Commentationes Mathematicae Universitatis Carolinae, Tome 52 (2011) no. 1, pp. 21-29. http://geodesic.mathdoc.fr/item/CMUC_2011__52_1_a1/