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