This article is cited in 4 papers

RESEARCH ARTICLE

Finite groups with a system of generalized central elements

Olga Shemetkova

Russian Economic Academy named after G. V. Plekhanov, Stremyanny per. 36, 113054 Moscow, Russia

Abstract: Let $H$ be a normal subgroup of a finite group $G$. A number of authors have investigated the structure of $G$ under the assumption that all minimal or maximal subgroups in Sylow subgroups of $H$ are well-situated in $G$. A general approach to the results of that kind is proposed in this article. The author has found the conditions for $p$-elements of $H$ under which $G$-chief $p$-factors of $H$ are $\mathfrak{F}$-central in $G$.

Keywords: finite group, $Qf$-central element, formation.

MSC: 20D10

Received: 12.04.2004
Revised: 06.12.2004

Language: English

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