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IMI/Publicaţii/QRS/Ediţii/QRS v.21, n.2 (30), 2013/

On Latin squares of polynomially complete quasigroups and quasigroups generated by shifts

Authors: V. A. Artamonov, S. Chakrabarti, S. Gangopadhyay and S. K. Pal

Abstract

We develop some methods and algorithms for checking the polynomial completeness property of some finite quasigroups by considering their corresponding Latin square representations. It is shown that polynomially complete quasigroups are simple and non-T-quasigroups. We study cyclic decompositions of permutations related to rows and columns of Latin squares of non-simple quasigroups and of T-quasigroups. Here we develop the criteria for the polynomial completeness of finite quasigroups based on this study.

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