on p-nilpotency of finite groups with ss-normal subgroups

A subgroup h of a group g is said to be ss-embedded in g if there exists a normal subgroup t of g such that ht is subnormal in g and h ∩ t ≤ hsg, where hsg is the maximal spermutable subgroup of g contained in h. we say that a subgroup h is an ss-normal subgroup in g if there exists a normal subgroup t of g such that g = ht and h ∩ t ≤ hss , where hss is an ss-embedded subgroup of g contained in h. in this paper, we study the influence of some ss-normal subgroups on the structure of a finite group g.