A. F. Vasil'ev, T. I. Vasilyeva, A. V. Syrokvashin, “A note on intersections of some maximal subgroups of finite groups”, PFMT, 2012, Issue 2(11),Pages <nobr>62

This article is cited in 9 papers

MATHEMATICS

A note on intersections of some maximal subgroups of finite groups

A. F. Vasil'ev^a, T. I. Vasilyeva^b, A. V. Syrokvashin^c

^a F. Scorina Gomel State University, Gomel
^b Belarusian State University of Transport, Gomel
^c I.G. Petrovsky Bryansk State University, Bryansk, Russia

Abstract: In the work V.S.Monahov's results that for any soluble non-nilpotent finite group $G$ its Frattini subgroup $\Phi(G)$ (subgroup $\Delta(G)$) coincides with intersection of all maximal (respectively all abnormal maximal) subgroups $M$ of group $G$ such that $MF(G) = G$, are extended on arbitrary finite groups.

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

UDC: 512.542

Received: 06.02.2012