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MATHEMATICS

On the intersection of all maximal $\mathfrak F$-subgroups of a finite group

A. N. Skiba

F. Skorina Gomel State University, Gomel

Abstract: Let $\mathfrak F$ be a class of groups. A subgroup $H$ of a group $G$ is said to be a maximal $\mathfrak F$-subgroup of $G$ if $H \in \mathfrak F$ and has no a subgroup $E \in \mathfrak F$ such that $H \le E$. The symbol $\Sigma_{\mathfrak F}(G)$ denotes the intersection of all maximal $\mathfrak F$-subgroups of $G$. We study the influence of the subgroup $\Sigma_{\mathfrak F}(G)$ on the structure of $G$.

Keywords: saturated formation, hereditary formation, minimal subgroup, maximal $\mathfrak F$-subgroup, $\mathfrak F$-hypercentre, soluble group, supersoluble group, $S$-quasinormal subgroup.

UDC: 512.542

Received: 22.07.2010

Language: English