Problemy Fiziki, Matematiki i Tekhniki (Problems of Physics, Mathematics and Technics)
 RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Archive Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 PFMT: Year: Volume: Issue: Page: Find

 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)
References: PDF file   HTML file
UDC: 512.542

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}