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Information × Registration Number 0211U001356, 0108U000624 , R & D reports Title The investigation of the structure of generalized soluble groups and the structure of modules over them popup.stage_title Head Kurdachenko Leonid, Доктор фізико-математичних наук Registration Date 31-01-2011 Organization Dniepropetrovsk national university popup.description2 The object of research - the structure of generalized solvable groups and related modules. The subject of research is infinite-dimensional linear groups and their associated modules over group rings and generalized soluble groups in which the important sub-systems have certain properties. The purpose of the work - study the influence of commuting, increases, pronormal systems of subgroups and their generalization to soluble and generalized soluble groups. Methods of research - the modern methods of group theory, ring theory and module theory. Obtained a description of periodic locally soluble FC - groups in which commutativity is a transitive property. Obtained the conditions under which a periodic locally soluble FC-group is the RT - group. Obtained necessary and sufficient conditions under which a periodic locally soluble FC - groups belong to the class of RT - groups. Obtained a relation between the properties of commutativity and pronormality in a class of periodic locally soluble FC - groups. Obtained a description of periodic locally soluble groups in which the property S - commutativity is transitive. Obtained necessary and sufficient conditions under which a periodic FC - groups belong to the class of PST - groups. It was investigated the structure of Chernikov PST - groups and the structure of PST - groups that belong to the SS - groups. It was described the periodic locally soluble CC - groups in which the property S - commutativity is transitive. Received tests on pronormality and theorems on the structure of infinite groups all of whose increasing subgroups are commute. It was proved theorems on the structure and properties of modules with restriction on cocentralizer of elements, and theorems on the structure and properties of modules with finite orbits. All results are new and are consistent with international standards temple on the subject. Product Description popup.authors Дашкова Ольга Юріївна Чупордя Василь Анатолійович popup.nrat_date 2020-04-02 Close