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Tr. Inst. Mat., 2008, Volume 16, Number 1, Pages 97–99 (Mi timb62)  

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

On finite groups with $Q$-central elements of prime order

O. L. Shemetkova

Plekhanov Russian State Academy of Economics, Moscow

Abstract: Following L. A. Shemetkov, an element $x$ of a non-nilpotent finite group $X$ is called a $Q$-central element if there exists a central chief factor $H/L$ of $X$ such that $x\in H$ and $x\notin L$. An element $x$ is called a $Q_8$-element in a group if there exists a section $A/B$ such that $A/B$ contains $xB$ and is isomorphic to the quaternion group $Q_8$ of order $8$, and $o(x)$ coincides with the order of $xB$ in $A/B$. Let $G$ be a finite group such that every its element of prime order is $Q$-central. Then the following conditions hold: 1) a Sylow 2-subgroup $G_2$ of $G$ is normal and $G/G_2$ is nilpotent; 2) there is a $Q_8$-element in $G_2$ which is not $Q$-central in $G$.

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UDC: 512.542
Received: 03.01.2008

Citation: O. L. Shemetkova, “On finite groups with $Q$-central elements of prime order”, Tr. Inst. Mat., 16:1 (2008), 97–99

Citation in format AMSBIB
\Bibitem{She08}
\by O.~L.~Shemetkova
\paper On finite groups with $Q$-central elements of prime order
\jour Tr. Inst. Mat.
\yr 2008
\vol 16
\issue 1
\pages 97--99
\mathnet{http://mi.mathnet.ru/timb62}


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    This publication is cited in the following articles:
    1. N. Yang, W. Guo, O. L. Shemetkova, “Finite groups with $S$-supplemented $p$-subgroups”, Siberian Math. J., 53:2 (2012), 371–376  mathnet  crossref  mathscinet  isi
  • Труды Института математики
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