On \(p\)-nilpotency of finite group with normally embedded maximal subgroups of some Sylow subgroups

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.