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.