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Bul. Acad. Ştiinţe Repub. Mold. Mat., 2014, Number 3, Pages 89–96 (Mi basm373)  

Near-totally conjugate orthogonal quasigroups

G. B. Belyavskayaa, T. V. Popovichb

a Institute of Mathematics and Computer Science, Academy of Sciences of Moldova, Academiei str. 5, MD-2028, Chişinău, Moldova
b A. Russo State University, Balti, Moldova

Abstract: The near-totally conjugate orthogonal quasigroups (near-$totCO$-quasigroups), i.e., quasigroups for which there exist five (but there are no six) pairwise orthogonal conjugates, are studied. We consider six types of such quasigroups, connection between them and prove that for any integer $n\geq7$ which is relatively prime to 2,3 and 5 there exist near-$totCO$-quasigroups of order $n$ of any type. Three types of conjugate orthogonality graphs, associated with these quasigroups are characterized.

Keywords and phrases: quasigroup, $T$-quasigroup, conjugate, parastrophe, conjugate orthogonal quasigroup, Latin square, graph of conjugate orthogonality.

Full text: PDF file (116 kB)
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Document Type: Article
MSC: 20N05, 05B15
Received: 11.09.2014
Language: English

Citation: G. B. Belyavskaya, T. V. Popovich, “Near-totally conjugate orthogonal quasigroups”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2014, no. 3, 89–96

Citation in format AMSBIB
\Bibitem{BelPop14}
\by G.~B.~Belyavskaya, T.~V.~Popovich
\paper Near-totally conjugate orthogonal quasigroups
\jour Bul. Acad. \c Stiin\c te Repub. Mold. Mat.
\yr 2014
\issue 3
\pages 89--96
\mathnet{http://mi.mathnet.ru/basm373}


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