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Information × Registration Number 0221U102156, 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 28-01-2021 Organization Oles Honchar Dnipro National University popup.description2  The objects of research 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 a description of Leibniz algebras with restrictions on the systems of their subalgebras. Obtain a description of some types of groups, with natural restrictions associated with section and special rank. Investigation of the influence of mutual analogues of substructures on the structure of algebraic structures in which they arise. Obtaining a new method for finding the eigenvalues of a self-adjoint operator taking into account the orthogonality of the states of the problem of quantum mechanics. As a result of research, the description of Leibniz algebras with restrictions on some systems of their subalgebras is received. Analogs of Hall's theorem for infinitely generated linear groups with restrictions related to section rank are obtained. Non-periodic generalized solvable groups whose cyclic subgroups are GNA-subgroups are described. Finitely generated linear groups of finite rank, which have exact irreducible primitive images over the field of characteristic 0, are studied. All the obtained results are new and correspond to the world level of scientific research. Scope of use – education, science. Product Description popup.authors Hlushkov Vitaliy M. Pypka Oleksandr O Tushev Anatolii V. Chupordia Vasil A. Yashchuk Viktoriia popup.nrat_date 2021-01-28 Close