Geodesic
Conjugate-orthogonality and the complete multiplication group of a~quasigroup
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2009), pp. 22-30

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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 pairs of conjugates for quasigroups (loops) from some classes. For finite quasigroups the quasi-identities corresponding to orthogonality of pairs of conjugates are given. 
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     title = {Conjugate-orthogonality and the complete multiplication group of a~quasigroup},
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G. Belyavskaya; A. Diordiev. Conjugate-orthogonality and the complete multiplication group of a~quasigroup. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2009), pp. 22-30. http://geodesic.mathdoc.fr/item/BASM_2009_1_a1/