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PFMT, 2011, Issue 1(6), Pages 57–61 (Mi pfmt85)  

MATHEMATICS

Criteria of $p$-supersolubility and supersolubility of finite groups

V. A. Kovaleva, A. N. Skiba

F. Skorina Gomel State University, Gomel

Abstract: Let $G$ be a finite group, $A$ a subgroup of $G$. Then we say that $A$ is generalized quasinormal in $G$ if $A$ either covers or avoids every maximal pair $(K,H)$ of $G$. We say that $A$ is $m$-supplemented in $G$ if $G$ has a subgroup $T$ and a generalized quasinormal subgroup $C$ such that $G = AT$ and $T \cap A \le C \le A$. Based on these concepts new characterizations of finite $p$-supersoluble and supersoluble groups are obtained.

Keywords: maximal pair, generalized quasinormal subgroup, $m$-supplemented subgroup, $p$-supersoluble group, supersoluble group.

Full text: PDF file (359 kB)
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UDC: 512.542
Received: 27.01.2011

Citation: V. A. Kovaleva, A. N. Skiba, “Criteria of $p$-supersolubility and supersolubility of finite groups”, PFMT, 2011, no. 1(6), 57–61

Citation in format AMSBIB
\Bibitem{KovSki11}
\by V.~A.~Kovaleva, A.~N.~Skiba
\paper Criteria of $p$-supersolubility and supersolubility of finite groups
\jour PFMT
\yr 2011
\issue 1(6)
\pages 57--61
\mathnet{http://mi.mathnet.ru/pfmt85}


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