This article is cited in 11 papers

$S$-embedded subgroups of finite groups

Wenbin Guo^ab, Yi Lu^b, Wenjuan Niu<sup>b

a</sup> Dep. Math., Univ. of Science and Technology of China, Hefei
^b Dep. Math., Xuzhou Normal Univ., Xuzhou

Abstract: 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, permutable group, $S$-embedded subgroup, supersoluble group, $p$-nilpotent group.

UDC: 512.542

Received: 08.09.2009

 English version: Algebra and Logic, 2010, 49:4, 293–304

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