Geodesic
Supersolvability of a finite group with $\mu X$-supplemented subgroups
Problemy fiziki, matematiki i tehniki, no. 1 (2011), pp. 84-88.

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Let $G$ be a finite group, $X$ – some non-empty subset of the group $G$. The subgroup $H$ of group $G$ is identified $\mu X$-supplemented in $G$ if there exists a subgroup $B$ such that $G = HB$ and for any maximal subgroup $H_1$ of $H$ there is $x \in X$ such that $H_1 B \ne G$ and $H_1 B^x = B^x H_1$. The $p$-supersolvability of a finite group with $\mu X$-supplemented Sylow $p$-subgroup for initial importance of the number $p$ are obtained. New conditions of the supersolvability finite groups is received.
Keywords: finite group, Sylow subgroup, $\mu X$-supplemented subgroup
Mots-clés : supersolvable group, $p$-supersolvable group. 
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A. V. Shnyparkov. Supersolvability of a finite group with $\mu X$-supplemented subgroups. Problemy fiziki, matematiki i tehniki, no. 1 (2011), pp. 84-88. http://geodesic.mathdoc.fr/item/PFMT_2011_1_a13/

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