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PFMT, 2019, Issue 3(40), Pages 63–66 (Mi pfmt656)  

MATHEMATICS

On $p$-supersolubility of one class finite groups

I. M. Dergacheva, E. A. Zadorozhnyuk, I. P. Shabalina

Belarusian State University of Transport, Gomel

Abstract: The following is proved: A finite group $G$ is $p$-supersoluble if and only if it has a normal subgroup $N$ with $p$-supersoluble quotient $G / N$ such that either $N$ is $p'$-group or $p$ divides $|N|$ and $|G : N_G(L)|$ equals to a power of $p$ for any cyclic $p$-subgroup $L$ of $N$ of order $p$ or order $4$ (if $p = 2$ and a Sylow $2$-subgroup of $N$ is non-abelian).

Keywords: finite group, $p$-nilpotent group, $p$-supersoluble group.

Full text: PDF file (326 kB)
References: PDF file   HTML file
UDC: 512.542
MSC: 20D10, 20D15
Received: 12.04.2019
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Citation: I. M. Dergacheva, E. A. Zadorozhnyuk, I. P. Shabalina, “On $p$-supersolubility of one class finite groups”, PFMT, 2019, no. 3(40), 63–66

Citation in format AMSBIB
\Bibitem{DerZadSha19}
\by I.~M.~Dergacheva, E.~A.~Zadorozhnyuk, I.~P.~Shabalina
\paper On $p$-supersolubility of one class finite groups
\jour PFMT
\yr 2019
\issue 3(40)
\pages 63--66
\mathnet{http://mi.mathnet.ru/pfmt656}


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