Geodesic
Near-totally conjugate orthogonal quasigroups
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2014), pp. 89-96.

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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≥7 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. 
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G. B. Belyavskaya; T. V. Popovich. Near-totally conjugate orthogonal quasigroups. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2014), pp. 89-96. https://geodesic-test.mathdoc.fr/item/BASM_2014_3_a8/

[1] Belousov V. D., “Parastrophic-orthogonal quasigroups”, Quasigroups and Related Systems, 13:1 (2005), 25–73 | MR

[2] Belyavskaya G. B., Popovich T. V., “Conjugate sets of loops and quasigroups. DC-quasigroups”, Bul. Acad. Ştiinţe Repub. Moldova. Mat., 2012, no. 1(59), 21–31 | MR | Zbl

[3] Belyavskaya G. B., Popovich T. V., “Totally conjugate orthogonal quasigroups and complete graphs”, Journal of Mathematical Sciences, 185:2 (2012), 184–191 | DOI | MR | Zbl

[4] Bennett F. E., “The spectra of a variety of quasigroups and related combinatorial designs”, Discrete mathematics, 77 (1989), 29–50 | DOI | MR | Zbl

[5] Bennett F. E., “Latin squares with pairwise orthogonal conjugates”, Discrete mathematics, 36 (1981), 117–137 | DOI | MR | Zbl

[6] Bennett F. E., “On conjugate orthogonal idempotent Latin squares”, Ars. combinatorica, 19 (1985), 37–50 | MR

[7] Bennett F. E., Mendelsohn N. S., “Conjugate orthogonal Latin square graphs”, Congressus Numerantium, 23 (1979), 179–192 | MR | Zbl

[8] Bennett F. E., Zhang Hantao, “Latin squares with self-orthogonal conjugates”, Discrete mathematics, 284 (2004), 45–55 | DOI | MR | Zbl

[9] Chaffer R. A., Lieberman D. J., Smith D. D., “The number of orthogonal conjugates of a quasigroup”, Congressus Numerantium, 35 (1982), 169–180 | MR | Zbl

[10] Evans T., “Algebraic structures associated with Latin squares and orthogonal arrays”, Congressus Numerantium, 13, Proc. Conf. Algebraic Aspects of Combinatorics (1975), 31–52 | MR

[11] Lindner C. C., Steedly D., “On the number of conjugates of a quasigroup”, Algebra Univ., 5 (1975), 191–196 | DOI | MR | Zbl

[12] Lindner C. C., Mendelsohn E., Mendelsohn N. S., Wolk B., “Orthogonal Latin square graphs”, J. Graph Theory, 3 (1979), 325–328 | DOI | MR

[13] Phelps K. T., “Conjugate orthogonal quasigroups”, J. Combin. Theory A, 25 (1978), 117–127 | DOI | MR | Zbl