On well \(p\)-embedded subgroups of finite groups

Abstract

Let \(G\) be a finite group, \(H\) a subgroup   of  \(G\) and \(H_{s G}\) the subgroup of \(H\) genarated by all those subgroups of \(H\) which are \(s\)-permutable in \(G\). Then we say that \(H\) is well \(p\)-embedded in \(G\) if \(G\) has a  quasinormal subgroup \(T\) such that \(HT=G\) and \(T\cap H\leq H_{s G}\). In the present article we use the well \(p\)-embedded groups to obtain new characterizations for some class of finite soluble, supersoluble, metanilpotent and dispersive groups.