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Ternary quasigroups and the modular group

Jonathan D. H. Smith (2008)

Commentationes Mathematicae Universitatis Carolinae

For a positive integer n , the usual definitions of n -quasigroups are rather complicated: either by combinatorial conditions that effectively amount to Latin n -cubes, or by 2 n identities on n + 1 different n -ary operations. In this paper, a more symmetrical approach to the specification of n -quasigroups is considered. In particular, ternary quasigroups arise from actions of the modular group.

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