This article is cited in 2 papers

Research articles

Conjugate-orthogonality and the complete multiplication group of a quasigroup

G. Belyavskaya^a, A. Diordiev

^a Institute of Mathematics and Computer Science, Academy of Sciences of Moldova, Chisinau, Moldova

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 pairs of conjugates for quasigroups (loops) from some classes. For finite quasigroups the quasi-identities corresponding to orthogonality of pairs of conjugates are given.

Keywords and phrases: quasigroup, loop, primitive quasigroup, quasi-identity, multiplication group, conjugate, parastrophe, conjugate-orthogonality.

MSC: 20N05, 20N15

Received: 17.07.2008

Language: English

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