Algebra and Discrete Mathematics - №2 - 2004 http://hdl.handle.net/123456789/93 2019-05-08T07:58:31Z A note to my paper “Multi-algebras from the viewpoint of algebraic logic” http://hdl.handle.net/123456789/112 A note to my paper “Multi-algebras from the viewpoint of algebraic logic” Cırulis, Janis The definition of a resolvent, introduced in the paper mentioned in the title, is simplified, and some misprints in that paper are corrected. 2003-01-01T00:00:00Z Groups, in which almost all subgroups are near to normal http://hdl.handle.net/123456789/111 Groups, in which almost all subgroups are near to normal Semko, M. M.; Kuchmenko, S. M. A subgroup H of a group G is said to be nearly normal, if H has a finite index in its normal closure. These sub- groups have been introduced by B.H. Neumann. In a present paper is studied the groups whose non polycyclic by finite subgroups are nearly normal. It is not hard to show that under some natural restrictions these groups either have a finite derived subgroup or belong to the class S1F (the class of soluble by finite minimax groups). More precisely, this paper is dedicated of the study of S1F groups whose non polycyclic by finite subgroups are nearly normal. 2004-01-01T00:00:00Z Generalized equivalence of collections of matrices and common divisors of matrices http://hdl.handle.net/123456789/110 Generalized equivalence of collections of matrices and common divisors of matrices Petrychkovych, Vasyl‘ M. The collections (A1, ...,Ak) and (B1, ...,Bk) of matrices over an adequate ring are called generalized equivalent if Ai = UBiVi for some invertible matrices U and Vi, i = 1, ..., k. Some conditions are established under which the finite collection consisting of the matrix and its the divisors is generalized equivalent to the collection of the matrices of the triangular and diagonal forms. By using these forms the common divisors of matrices is described. 2004-01-01T00:00:00Z On autotopies and automorphisms of n-ary linear quasigroups http://hdl.handle.net/123456789/109 On autotopies and automorphisms of n-ary linear quasigroups Marini, Alberto; Shcherbacov, Victor In this article we study structure of autotopies, automorphisms, autotopy groups and automorphism groups of n- ary linear quasigroups. We find a connection between automorphism groups of some special kinds of n-ary quasigroups (idempotent quasigroups, loops) and some isotopes of these quasigroups. In binary case we find more detailed connections between automorphism group of a loop and automorphism group of some its isotope. We prove that every finite medial n-ary quasigroup of order greater than 2 has a non- identity automorphism group. We apply obtained results to give some information on auto- morphism groups of n-ary quasigroups that correspond to the ISSN code, the EAN code and the UPC code. 2004-01-01T00:00:00Z