RESEARCH ARTICLE

On $p$-nilpotency of finite group with normally embedded maximal subgroups of some Sylow subgroups

A. Trofimuk

Department of Mathematics, Gomel Francisk Skorina State University, Gomel 246019, Belarus

Abstract: 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: $p$-supersolvable group, normally embedded subgroup, maximal subgroup, Sylow subgroup.

MSC: 20D10

Received: 21.04.2018

Language: English

DOI: 10.12958/adm1128

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