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.