This article is cited in 10 papers

On orthogonality of binary operations and squares

Gary L. Mullen^a, Victor A. Shcherbacov<sup>b

a</sup> Department of Mathematics, Pennsylvania State University, University Park, USA
^b Institute of Mathematics and Computer Science, Academy of Sciences of Moldova, Chisinau, Moldova

Abstract: Orthogonality of a pair of binary groupoids, left quasigroups and quasigroups from some points of view is studied. Necessary and sufficient conditions of orthogonality of a finite quasigroup and any its parastrophe (conjugate quasigroup in other terminology), including ones in language of quasi-identities, are given. New concept of gisotopy, which generalizes the concept of isotopy, is defined. There is information on quasigroups with self-orthogonal conjugates.

Keywords and phrases: Groupoid, left quasigroup, quasigroup, Latin square, row-Latin square, Latin square with self-orthogonal conjugates, orthogonality, parastrophy, isotopy, isostrophy, gisotopy.

MSC: 20N05, 05B15, 20N02, 08C15

Received: 16.07.2005

Language: English

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