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Tr. Inst. Mat., 2016, Volume 24, Number 1, Pages 34–37 (Mi timb256)  

This article is cited in 1 scientific paper (total in 1 paper)

On permutability of $n$-maximal subgroups with $p$-nilpotent Schmidt subgroups

V. N. Kniahina

Gomel Engineering Institute, Ministry of Extraordinary Situations of the Republic of Belarus

Abstract: A Schmidt group is a finite nonnilpotent group in which every proper subgroup is nilpotent. Fix a positive integer $n.$ Let $G$ be a solvable group. Suppose that each $n$-maximal subgroup of $G$ is permutable with every $p$-nilpotent Schmidt subgroup. We prove that if $n\in\{1,2,3\},$ then $G/F(G)$ is $p$-closed, where $F(G)$ is the Fitting subgroup of $G$.

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UDC: 512.542
Received: 21.04.2016

Citation: V. N. Kniahina, “On permutability of $n$-maximal subgroups with $p$-nilpotent Schmidt subgroups”, Tr. Inst. Mat., 24:1 (2016), 34–37

Citation in format AMSBIB
\Bibitem{Kny16}
\by V.~N.~Kniahina
\paper On permutability of $n$-maximal subgroups with $p$-nilpotent Schmidt subgroups
\jour Tr. Inst. Mat.
\yr 2016
\vol 24
\issue 1
\pages 34--37
\mathnet{http://mi.mathnet.ru/timb256}


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    This publication is cited in the following articles:
    1. E. V. Zubei, “O razreshimosti konechnoi gruppy s polunormalnymi ili subnormalnymi podgruppami Shmidta nekotoroi ee maksimalnoi podgruppy”, Tr. IMM UrO RAN, 25, no. 1, 2019, 55–61  mathnet  crossref  elib
  • Труды Института математики
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