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Information × Registration Number 0220U101520, 0119U100373 , R & D reports Title An investigation of algebraic structures with natural restrictions and some questions of quantum mechanics popup.stage_title Head Kurdachenko Leonid A., Доктор фізико-математичних наук Registration Date 12-02-2020 Organization Oles Honchar Dnipro National University popup.description2  The objects of study are algebras (Lie algebras and Leibniz algebras and other types of algebras), groups, some types of linear groups, and modules over group rings. The aim of the work is to obtain a description of Leibniz algebras of small dimensions over fields of characteristic 0, and over finite fields, the development of the theory of generalized nilpotent and generalized solvable Leibniz algebras, obtaining descriptions of certain types of groups, with natural restrictions on the systems of their subgroups, Investigation of the influence of mutual analogues of substructures on the structure of algebraic structures in which they arise. Research methods - modern methods of the theory of groups, rings and modules. As a result of the research, a description of Leibniz algebras with restrictions on some systems of their subalgebras is obtained. An analysis is made of the approach to the study of Leibniz algebras, which is based on the concept of anticenter and antinilpotency. We describe the Leibniz algebras of dimension 3. It was obtained a description of the structure of some groups with restrictions on the systems of subgroups. Criteria of primitiveness of group algebras of some classes of locally soluble groups are obtained. All the results obtained are new and correspond to the world level of scientific research. Product Description popup.authors Glushkov Vitaly M. Pypka Oleksandr O. Tushev Anatolii V. Chupordia Vasil A. Yashchuk Viktoriia S. popup.nrat_date 2020-04-02 Close