Geodesic
On the intersection of all maximal $\mathfrak F$-subgroups of a finite group
Problemy fiziki, matematiki i tehniki, no. 3 (2010), pp. 56-62

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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, supersoluble group, $S$-quasinormal subgroup.
Mots-clés : soluble group 
@article{PFMT_2010_3_a8,
     author = {A. N. Skiba},
     title = {On the intersection of all maximal $\mathfrak F$-subgroups of a finite group},
     journal = {Problemy fiziki, matematiki i tehniki},
     pages = {56--62},
     publisher = {mathdoc},
     number = {3},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PFMT_2010_3_a8/}
}
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A. N. Skiba. On the intersection of all maximal $\mathfrak F$-subgroups of a finite group. Problemy fiziki, matematiki i tehniki, no. 3 (2010), pp. 56-62. http://geodesic.mathdoc.fr/item/PFMT_2010_3_a8/