Groups with Chernikov conjugacy classes in which Sylow permutability is a transitive relation

A subgroup H of a periodic group G is said to be Sylow permutable in G if HS=SH for every Sylow subgroup S of G. Like normality, Sylow permutability is not a transitive relation. In this paper we characterize periodic locally soluble groups with Chernikov conjugacy classes (periodic locally soluble CC-groups) in which Sylow permutability is a transitive relation (PST-groups) describing their structure in a very detailed way then extending the structure of finite soluble PST-groups. Moreover we give an effective construction of these groups.