Shahrood University of Technology Journal of Algebraic Systems 2345-5128 4 1 2016 09 01 ON FINITE GROUPS IN WHICH SS-SEMIPERMUTABILITY IS A TRANSITIVE RELATION 29 36 726 10.22044/jas.2016.726 EN S.E. Mirdamadi Department of Mathematics, University of Shahrekord, P.O.Box 115, Shahrekord, Iran. Gh.R Rezaeezadeh Department of Mathematics, University of Shahrekord, P.O.Box 115, Shahrekord, Iran. Journal Article 2015 10 21 Let H be a subgroup of a finite group G. We say that H is SS-semipermutable in G<br />if H has a supplement K in G such that H permutes with every Sylow subgroup X of K<br />with (jXj; jHj) = 1. In this paper, the Structure of SS-semipermutable subgroups, and finite<br />groups in which SS-semipermutability is a transitive relation are described. It is shown that<br />a finite solvable group G is a PST-group if and only if whenever H  K are two p-subgroups<br />of G, H is SS-semipermutable in NG(K). https://jas.shahroodut.ac.ir/article_726_4dada44a60bbc33404cb7f7dcf783e40.pdf