Оn construction of n -ary quasigroups.
Keywords:
complete permutation, disjoint permutations, near disjoint permutations, isotope of a quasigroup, perpendicularity of quasigroupsAbstract
In this article the relationships among complete permutations of isotopic quasigroups are described, a criterion of existence of orthogonal mate is specified, the necessary and sufficient conditions for orthogonality of torsion quasigroups are found. For solving the problem of construction of n -ary quasigroups which are decomposed into a composition of two quasigroups, some necessary statements are proved. For this goal algorithms of construction of quasigroups which have admissible binary retracts are proposed, method of construction of pair of perpendicular quasigroups of the same arity are found.References
Белоусов В.Д. Системы ортогональних операций / В.Д. Белоусов // Математический сборник. – 1968. – Т.77 (119). – С .38-58.
Белявская Г.Б. О допустимости квазигрупп / Г.Б. Белявская, А.Ф. Руссу // Математические исследования. – 1975. – № 10, вып. 1. – C. 45-57.
Глухов М.М. Об -замкнутых класах и -полных системах функцій k -значной логики / M.M. Глухов // Дискретная математика. – 1989. – № 1. – С.16-21.
Оной В.И. n -Арные лупы со свойствами обратимости с одним параметром обращения / В.И. Оной, Л.А.Урсу // Квазигруппы и их системы, Кишинев ``Штиинца''. – 1990. – C. 72-82.
Сохацкий Ф.М. Многоместные разделимые квазигруппы со свойством обратимости // Математические исследования (Квазигруппы и их системы). – 1990. – вып. 113. – C. 89-99.
Evans A.B., Applications of complete mappings and ortomorphisms of finite groups / A.B Evans // Quasigroups and related systems. – 2015. – N 23, P. 5-30.
Keedwell A.D., Denes J. Latin Squares and their Applications / A.D. Keedwell, J. Denes. – Budapest: Academiai Kiado, 2015. – 545 p.
Krotov D.S. On irreducible n -ary quasigroups with reducible retracts / D.S. Krotov // European J. Comb. – 2008. – V. 29, N. 2. P. 507-513.
Krotov D.S. On reconstructing reducible n -ary quasigroups and switching subquasigroups / D.S. Krotov, V.N. Potapov, P.V.Sokolova // Quasigroups and Related Systems. – 2008. – V. 16, N 1. – P. 55-67.
Krotov D.S. Constructions of transitive latin hypercubes / D.S. Krotov, V.N. Potapov // arXiv:1303.0004v2 [cs.IT] 4 May 2015. – 16 p.
Paige L.J. Complete mappings of finite groups / L.J. Paige // Pacific J. Math. – 1951. – N 1. P. 111-116.
Sokhatsky F.M. Invertibility criterion of composition of two multiary quasigroups, / F.M. Sokhatsky, I.V. Fryz // Comment. Math. Univ. Carolin. – 2012. – N 53, 3. 429-445.
