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.
Fulltext:
PDF file (116 kB)