ON p-NILPOTENCY OF FINITE GROUPS

Abstract

A subgroup H of a finite group G is said to be weakly s-supplemently embedded subgroup in G if there exists a subgroup T of G such that G = HT and H ∩ T ≤ H_se, where H_se is an s-quasinormally embedded subgroup of G contained in H.  In this paper we investigate the structure of G under the assumption that some subgroups of P are weakly s-supplemently embedded in G, and some new criteria are obtained.