http://dspace.nbuv.gov.ua:80/handle/123456789/188575 Tue, 21 Apr 2026 09:17:17 GMT 2026-04-21T09:17:17Z http://dspace.nbuv.gov.ua:80/bitstream/id/564387/ http://dspace.nbuv.gov.ua:80/handle/123456789/188575 http://dspace.nbuv.gov.ua:80/handle/123456789/188713 The center of the wreath product of symmetric group algebras Tout, O. We consider the wreath product of two symmetric groups as a group of blocks permutations and we study its conjugacy classes. We give a polynomiality property for the structure coefficients of the center of the wreath product of symmetric group algebras. This allows us to recover an old result of Farahat and Higman about the polynomiality of the structure coefficients of the center of the symmetric group algebra and to generalize our recent result about the polynomiality property of the structure coefficients of the center of the hyperoctahedral group algebra. Fri, 01 Jan 2021 00:00:00 GMT http://dspace.nbuv.gov.ua:80/handle/123456789/188713 2021-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/188712 Semisymmetric Zp-covers of the graph C20 Talebi, A.A.; Mehdipoor, N. A graph X is said to be G-semisymmetric if it is regular and there exists a subgroup G of A := Aut(X) acting transitively on its edge set but not on its vertex set. In the case of G = A, we call X a semisymmetric graph. Finding elementary abelian covering projections can be grasped combinatorially via a linear representation of automorphisms acting on the first homology group of the graph. The method essentially reduces to finding invariant subspaces of matrix groups over prime fields. In this study, by applying concept linear algebra, we classify the connected semisymmetric Zp-covers of the C20 graph. Fri, 01 Jan 2021 00:00:00 GMT http://dspace.nbuv.gov.ua:80/handle/123456789/188712 2021-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/188711 Semi-lattice of varieties of quasigroups with linearity Sokhatsky, F.M.; Krainichuk, H.V.; Sydoruk, V.A. A σ-parastrophe of a class of quasigroups 𝕬 is a class σ𝕬 of all σ-parastrophes of quasigroups from 𝕬. A set of all pairwise parastrophic classes is called a parastrophic orbit or a truss. A parastrophically closed semi-lattice of classes is a bunch. A linearity bunch is a set of varieties which contains the variety of all left linear quasigroups, the variety of all left alinear quasi-groups, all their parastrophes and all their intersections. It contains 14 varieties, which are distributed into six parastrophic orbits. All quasigroups from these varieties are called dilinear. To obtain all varieties from the bunch, concepts of middle linearity and middle alinearity are introduced. A well-known identity or a system of identities which describes a variety from every parastrophic orbit of the bunch is cited. An algorithm for obtaining identities which describe all varieties from the parastrophic orbits is given. Examples of quasigroups distinguishing one variety from the other are presented. Fri, 01 Jan 2021 00:00:00 GMT http://dspace.nbuv.gov.ua:80/handle/123456789/188711 2021-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/188710 Clean coalgebras and clean comodules of finitely generated projective modules Puspita, N.P.; Wijayanti, I.E.; Surodjo, B. Let R be a commutative ring with multiplicative identity and P is a finitely generated projective R-module. If P* is the set of R-module homomorphism from P to R, then the tensor product P* ⊗R P can be considered as an R-coalgebra. Furthermore, P and P* is a comodule over coalgebra P* ⊗R P. Using the Morita context, this paper give sufficient conditions of clean coalgebra P* ⊗R P and clean P* ⊗R P-comodule P and P*. These sufficient conditions are determined by the conditions of module P and ring R. Fri, 01 Jan 2021 00:00:00 GMT http://dspace.nbuv.gov.ua:80/handle/123456789/188710 2021-01-01T00:00:00Z