Distributive and Anti-distributive Mendelsohn Triple Systems

Canadian mathematical bulletin

David Stanovský⁴  Terry S. Griggs¹  Diane M. Donovan²  Thomas A. McCourt³  Jakub Opršal⁴ 

[1] Department of Mathematics and Statistics, The Open University, Walton Hall, Milton Keynes MK7 6AA, UNITED KINGDOM;Centre for Discrete Mathematics and Computing, University of Queensland, St Lucia 4072, AUSTRALIA;School of Computing and Mathematics, Plymouth University, Drake Circus, Plymouth PL4 8AA, UNITED KINGDOM and Heilbronn Institute for Mathematical Research, University of Bristol, University Walk, Bristol BS8 1TW, UNITED KINGDOM;Department of Algebra, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 18675 Praha 8, CZECH REPUBLIC

关键词: Mendelsohn triple system;    quasigroup;    distributive;    Moufang loop;    Loeschian numbers;   

DOI  :  10.4153/CMB-2015-053-2

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

We prove that the existence spectrum of Mendelsohn triple systems whose associated quasigroups satisfy distributivity corresponds to the Loeschian numbers, and provide some enumeration results. We do this by considering a description of the quasigroups interms of commutative Moufang loops.In addition we provide constructions of Mendelsohn quasigroups that fail distributivity for as many combinations of elementsas possible. These systems are analogues of Hall triple systems and anti-mitreSteiner triple systems respectively.

【 授权许可】

Unknown