S.E. Mirdamadi - Department of Mathematics, University of Shahrekord, P.O.Box ۱۱۵, Shahrekord, Iran.
Gh.R Rezaeezadeh - Department of Mathematics, University of Shahrekord, P.O.Box ۱۱۵, Shahrekord, Iran.

Let H be a subgroup of a finite group G. We say that H is SS-semipermutable in Gif H has a supplement K in G such that H permutes with every Sylow subgroup X of Kwith (jXj; jHj) = 1. In this paper, the Structure of SS-semipermutable subgroups, and finitegroups in which SS-semipermutability is a transitive relation are described. It is shown thata finite solvable group G is a PST-group if and only if whenever H K are two p-subgroupsof G, H is SS-semipermutable in NG(K).

SS-semipermutable subgroups, S-semipermutable subgroups, PST-groups