This article is cited in 6 papers

Finite groups with $C$-quasinormal subgroups

A. N. Skiba^a, O. V. Titov<sup>b

a</sup> Francisk Skorina Gomel State University
^b Belarusian State University of Transport

Abstract: Consider some finite group $G$ and a finite subgroup $H$ of $G$. Say that $H$ is $c$-quasinormal in $G$ if $G$ has a quasinormal subgroup $T$ such that $HT=G$ and $T\cap H$ is quasinormal in $G$. Given a noncyclic Sylow subgroup $P$ of $G$, we fix some subgroup $D$ such that $1<|D|<|P|$ and study the structure of $G$ under the assumption that all subgroups $H$ of $P$ of the same order as $D$, having no supersolvable supplement in $G$, are $c$-quasinormal in $G$.

Keywords: Sylow subgroup, supplement to a subgroup, supersolvable group, quasinormal subgroup, saturated formation.

UDC: 512.54

Received: 22.06.2006
Revised: 04.02.2007

 English version: Siberian Mathematical Journal, 2007, 48:3, 544–554

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