http://dspace.nbuv.gov.ua:80/handle/123456789/150328 2026-04-18T16:19:43Z http://dspace.nbuv.gov.ua:80/handle/123456789/155728 Gyrogroups and left gyrogroups as transversals of a special kind Kuznetsov, E. In this article we study gyrogroups and left gyrogroups as transversals in some suitable groups to its subgroups. These objects were introduced into consideration in a connection with an investigation of analogies between symmetries in the classical mechanics and in the relativistic one. The author introduce some new notions into consideration (for example, a weak gyrotransversal) and give a full description of left gyrogroups (and gyrogroups) in terms of transversal identities. Also he generalize a construction of a diagonal transversal and obtain a set of new examples of left gyrogroups. 2003-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/155727 On equivalence of some subcategories of modules in Morita contexts Kashu, A.I. 2003-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/155704 On a group theoretical construction of expanding graphs Ustimenko, V.A. 2003-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/155703 On the separability of the restriction functor Theohari-Apostolidi, Th.; Vavatsoulas, H. Let G be a group, Λ = L σ∈G Λσ a strongly graded ring by G, H a subgroup of G and ΛH = L σ∈H Λσ. We give a necessary and sufficient condition for the ring Λ/ΛH to be separable, generalizing the corresponding result for the ring extension Λ/Λ1. As a consequence of this result we give a condition for Λ to be a hereditary order in case Λ is a strongly graded by finite group R-order in a separable K-algebra, for R a Dedekind domain with quotient field K. 2003-01-01T00:00:00Z