On well p-embedded subgroups of finite groups

Abstract

Let G be a finite group, H a subgroup of G and HsG the subgroup of H genarated by all those subgroups of H which are s-permutable in G. Then we say that H is well pembedded in G if G has a quasinormal subgroup T such that HT = G and T ∩ H ≤ HsG. In the present article we use the well pembedded groups to obtain new characterizations for some class of finite soluble, supersoluble, metanilpotent and dispersive groups.