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IMCS/Publications/BASM/Issues/BASM n.1 (59), 2009/

Conjugate-orthogonality and the complete multiplication group of a quasigroup.

Authors: Beliavscaia Galina, A. Diordiev

Abstract

In this note we establish connections between the orthogonality of conjugates of a finite or infinite quasigroup and some strictly transitive subsets of the complete multiplication group of this quasigroup. These connections are used for the investigation of orthogonality of distinct airs of conjugates for quasigroups (loops) from some classes. For finite quasigroups the quasiidentities corresponding to orthogonality of pairs of conjugates are given.

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