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PFMT, 2017, Issue 3(32), Pages 61–65 (Mi pfmt520)  

MATHEMATICS

On $\sigma$-permutable subgroups of finite groups

V. M. Selkin, A. N. Skiba

F. Scorina Gomel State University

Abstract: Let $\{\sigma_i \mid i\in I\}$ be some partition of the set of all primes $\mathbb{P}$ and let $G$ be a finite group. $G$ is said to be $\sigma$-full if $G$ has a Hall $\sigma_i$-subgroup for all $i$. A subgroup $A$ of $G$ is said to be $\sigma$-permutable in $G$ if $G$ is $\sigma$-full and $A$ permutes with all Hall $\sigma_i$-subgroups $H$ of $G$ (that is, $AH=HA$) for all $i$. In this paper, we give a survey of some recent results on $\sigma$-permutable subgroups of finite groups.

Keywords: finite group, a Robinson $\sigma$-complex of a group, $\sigma$-permutable subgroup, $\sigma$-soluble group, $\sigma$-supersoluble group, $\sigma$-CS-group.

Full text: PDF file (345 kB)
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UDC: 512.542
Received: 14.06.2017
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Citation: V. M. Selkin, A. N. Skiba, “On $\sigma$-permutable subgroups of finite groups”, PFMT, 2017, no. 3(32), 61–65

Citation in format AMSBIB
\Bibitem{SelSki17}
\by V.~M.~Selkin, A.~N.~Skiba
\paper On $\sigma$-permutable subgroups of finite groups
\jour PFMT
\yr 2017
\issue 3(32)
\pages 61--65
\mathnet{http://mi.mathnet.ru/pfmt520}


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