Geodesic
$S$-embedded subgroups of finite groups
Algebra i logika, Tome 49 (2010) no. 4, pp. 433-450.

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A subgroup $H$ of $G$ is said to be $S$-embedded in $G$ if $G$ has a normal subgroup $N$ such that $HN$ is $s$-permutable in $G$ and $H\cap N\le H_{sG}$, where $H_{sG}$ is the largest $s$-permutable subgroup of $G$ contained in $H$. $S$-embedded subgroups are used to give novel characterizations for some classes of groups. New results are obtained and a number of previously known ones are generalized.
Keywords: finite group, $S$-embedded subgroup, supersoluble group, $p$-nilpotent group.
Mots-clés : permutable group 
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Wenbin Guo; Yi Lu; Wenjuan Niu. $S$-embedded subgroups of finite groups. Algebra i logika, Tome 49 (2010) no. 4, pp. 433-450. http://geodesic.mathdoc.fr/item/AL_2010_49_4_a0/

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