the influence of h -subgroups on p-nilpotency and p-supersolvability of finite groups

Let g be a finite group. a subgroup h of g is an h -subgroup in g if ng(h) ∩ hg ≤ hfor any g ∈ g. in this article, by using the concept of h -subgroups, we study the influence of theintersection of op(g∗p) and the members of some fixed md(p) on the structure of the group g, wherep is a sylow p-subgroup of g. some new criteria for a group to be p-nilpotent and p-supersolvable aregiven and some recent results are extended and generalized