Тurbay N. Studying of the structure of the groups by the property of subgroups near to normal

The system of normal and near normal subgroups of group great influence on the structure of the group. The natural generalization of normal subgroups is permutable subgroups. That's why the most part of this dissertation is devoted to studying of periodic locally soluble FC - groups in which permutability is a transitive relation. We obtain the series of characterisations of PT - groups and describing the structure of periodic locally soluble FC - groups in which permutability is a transitive relation. S - permutability is a rather wide generalization of usual permutability. That's why the next step is studying of infinite PST - groups. In particularly, we obtain description of periodic locally soluble groups in which permutability is a transitive relation. In this paper we consider the relationship between properties permutability and S - permutability. The structure of Chernikov PST - groups and PST - groups from class of CC - groups are investigated. And we obtain full description of periodic locally soluble groups with Chernikov conjugacy classes in which Sylow permutability is a transitive relation.