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On $p$-nilpotency of finite group with normally embedded maximal subgroups of some Sylow subgroups
Algebra and discrete mathematics, Tome 29 (2020) no. 1, pp. 139-146.

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Let $G$ be a finite group and $P$ be a $p$-subgroup of $G$. If $P$ is a Sylow subgroup of some normal subgroup of $G$, then we say that $P$ is normally embedded in $G$. Groups with normally embedded maximal subgroups of Sylow $p$-subgroup, where ${(|G|, p-1)=1}$, are studied. In particular, the $p$-nilpotency of such groups is proved.
Keywords: normally embedded subgroup, maximal subgroup, Sylow subgroup.
Mots-clés : $p$-supersolvable group 
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A. Trofimuk. On $p$-nilpotency of finite group with normally embedded maximal subgroups of some Sylow subgroups. Algebra and discrete mathematics, Tome 29 (2020) no. 1, pp. 139-146. http://geodesic.mathdoc.fr/item/ADM_2020_29_1_a12/

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