Near-totally conjugate orthogonal quasigroups
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BELEAVSCAIA, Galina, POPOVICI, Tatiana. Near-totally conjugate orthogonal quasigroups. In: Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2014, nr. 3(76), pp. 89-96. ISSN 1024-7696.
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Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
Numărul 3(76) / 2014 / ISSN 1024-7696 /ISSNe 2587-4322

Near-totally conjugate orthogonal quasigroups
CZU: 512.548.7

Pag. 89-96

Beleavscaia Galina1, Popovici Tatiana2
 
1 Institute of Mathematics and Computer Science ASM,
2 "Alecu Russo" State University of Balti
 
 
Disponibil în IBN: 29 mai 2015


Rezumat

The near-totally conjugate orthogonal quasigroups (near-totCO-quasi- groups), 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.

Cuvinte-cheie
quasigroup, T-quasigroup, conjugate, parastrophe, Latin square,

conju- gate orthogonal quasigroup, graph of conjugate orthogonality.