Geodesic
The influence of weakly $s$-permutably embedded subgroups on the $p$-nilpotency of finite groups
Algebra and discrete mathematics, Tome 12 (2011) no. 1, pp. 20-27.

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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 of finite groups.
Keywords: weakly $s$-permutably embedded subgroups; $p$-nilpotent; maximal subgroup; 2-maximal subgroup. 
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Changwen Li. The influence of weakly $s$-permutably embedded subgroups on the $p$-nilpotency of finite groups. Algebra and discrete mathematics, Tome 12 (2011) no. 1, pp. 20-27. http://geodesic.mathdoc.fr/item/ADM_2011_12_1_a1/

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