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Latin squares over quasigroups. (English) Zbl 1451.05030
In this paper, the authors describe a constructive way for generating finite quasigroups of any given order that generalizes a previous method defined in [V. A. Nosov and A. E. Pankratiev, J. Math. Sci., New York 149, No. 3, 1230–1234 (2008; Zbl 1146.05011); translation from Fundam. Prikl. Mat. 12, No. 3, 65–71 (2006)]. Unlike that work, where they made use of proper families of functions over abelian groups, the new construction is based on proper families of functions over quasigroups and 3-quasigroups. In addition, unlike the previous proposal, the new one enables one to generate finite quasigroups containing no subquasigroups.
MSC:
05B15 Orthogonal arrays, Latin squares, Room squares
20N05 Loops, quasigroups
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