On Φ-τ-Supplement Subgroups of Finite Groups

Let τ be a subgroup functor and H a p-subgroup of a finite group G. Let G= G/Hand H= H/H. We say that H is Φ-τ-supplement in G if G has a subnormal subgroup T and a τ-subgroup S contained in H such that G=H T and H∩T≤SΦ(H). In this paper,some new characterizations of hypercyclically embedability and p-nilpotency of a finite group are obtained based on the assumption that some primary subgroups are Φ-τ-supplement in G.