G. R. REZAEEZADEH - Department of Mathematics, University of Shahrekord, P.O.Box ۱۱۵, Shahrekord, Iran.
Z. AGHAJARI - Department of Mathematics, University of Shahrekord, P.O.Box ۱۱۵, Shahrekord, Iran.

Abstract. A subgroup H of a group G is said to be SS-embeddedin G if there exists a normal subgroup T of G such that HT issubnormal in G and H T ≤ H sG , where H sG is the maximal s-permutable subgroup of G contained in H. We say that a subgroupH is an SS-normal subgroup in G if there exists a normal subgroupT of G such that G = HT and H T ≤ H SS , where H SS is anSS-embedded subgroup of G contained in H. In this paper, westudy the influence of some SS-normal subgroups on the structureof a finite group G.

SS-normal subgroup, SS-embedded subgroup, p-nilpotent group