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PFMT, 2019, Issue 1(38), Pages 50–55 (Mi pfmt622)  

MATHEMATICS

On some characterization of general Frattini subgroup of finite soluble group

S. F. Kamornikova, O. L. Shemetkovab

a F. Scorina Gomel State University
b Plekhanov Russian University of Economics, Moscow

Abstract: Let $G$ be a finite soluble group, $\theta$ be a regular subgroup $m$-functor, and $\Phi_\theta(G)$ be the intersection of all maximal $\theta$-subgroups of $G$. Let $n$ be the length of a $G$-series of the group $\mathrm{Soc}(G/\Phi_\theta(G))$, and $k$ be the number of central $G$-chief factors of this series. We prove that in this case $G$ contains $4n-3k$ maximal $\theta$-subgroups whose intersection is $\Phi_\theta(G)$.

Keywords: finite soluble group, maximal subgroup, Frattini $\theta$-subgroup.

Full text: PDF file (357 kB)
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UDC: 512.542
Received: 02.01.2019

Citation: S. F. Kamornikov, O. L. Shemetkova, “On some characterization of general Frattini subgroup of finite soluble group”, PFMT, 2019, no. 1(38), 50–55

Citation in format AMSBIB
\Bibitem{KamShe19}
\by S.~F.~Kamornikov, O.~L.~Shemetkova
\paper On some characterization of general Frattini subgroup of finite soluble group
\jour PFMT
\yr 2019
\issue 1(38)
\pages 50--55
\mathnet{http://mi.mathnet.ru/pfmt622}


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