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Information × Registration Number 0218U002195, 0115U002395 , R & D reports Title Generalized soluble groups and modules over them, and their application to other algebraic structures popup.stage_title Head Kurdachenko Leonid, Доктор фізико-математичних наук Registration Date 30-01-2018 Organization Oles Honchar Dnipro National University popup.description2 The object of research: the influence of important subgroups, factor groups, and automorphism groups on the structure of groups, associated with them modules over group rings that satisfy important natural restrictions, and also the application of these results to the study of certain types of semigroups. The aim of research: the creation of a theory of generalized nilpotent groups, in particular, finding the relationships of the commutant and its generalizations with the factor group on the center or its generalizations, and also finding the relationships of the lower hypocentre and its generalizations with the factor group over the upper hypercenter or its generalizations; the creation of new methods based on the studies of the corresponding classes of modules over group rings; a study of new types of semigroups associated with the set of all mappings from the group to the lattice. Methods of research are modern methods of the theory of groups, rings, modules and algebras. It is proved that the class of locally finite groups, each of which is an extension of a divisible group by means of a bounded group, is a Schur class and a Baer class. A modular analogue of Schur's theorem for modules over group rings of groups of finite section rank is obtained. An analogue of Baer's theorem is obtained for the Leibniz algebra. Numerical invariants characterizing the hypercentral residual for groups with quotient group by the hypercentre has finite rank, are obtained. The conditions for the existence of direct decompositions, in one part of which all generalized central factors are concentrated, and in the other - all generalized eccentric factors, are obtained. It was obtained a description of locally finite and certain classes of nonperiodic groups whose finitely generated subgroups are either permutable or prornormal. It was obtained a description of certain groups whose finitely generated subgroups are either commutative or weakly pronormal. A complete description of locally soluble groups, all subgroups of which are either almost normal or contranormal, is obtained. It was also obtained a description of locally soluble groups, all subgroups of which are either almost normal or abnormal. All results are new and meet the highest international standards in the subject. Scientific results introduce in the tutorial process. Scope: science and education. Product Description popup.authors Пипка Олександр Олександрович Чупордя Василь Анатолійович Ящук Вікторія Сергіївна popup.nrat_date 2020-04-02 Close