Some new characterizations of PST-groups

Abstract

Let H and B be subgroups of a finite group G such that G = NG(H)B. Then we say that H is quasipermutable (respectively S-quasipermutable) in G provided H permutes with B and with every subgroup (respectively with every Sylow subgroup) A of B such that (|H|, |A|) = 1. In this paper we analyze the influence of S-quasipermutable and quasipermutable subgroups on the structure of G. As an application, we give new characterizations of soluble P ST-groups.