Abstract
We propose a construction that allows generating large families of Latin squares, i.e., Cayley tables of finite quasigroups. This construction generalizes proper families of functions over Abelian groups introduced by Nosov and Pankratiev. We also show that all quasigroups generated by the original construction contain at least one subquasigroup, while the generalized construction generates quasigroups free of subquasigroups.
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ACKNOWLEDGMENTS
The authors are grateful to professor V.A. Artamonov for fruitful discussions.
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Galatenko, A.V., Nosov, V.A. & Pankratiev, A.E. Latin Squares over Quasigroups. Lobachevskii J Math 41, 194–203 (2020). https://doi.org/10.1134/S1995080220020079
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DOI: https://doi.org/10.1134/S1995080220020079