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Keywords:
quasigroup; ternary quasigroup; $n$-quasigroup; heterogeneous algebra; hyperidentity; modular group; conjugate; parastrophe; time reversal
quasigroup; ternary quasigroup; $n$-quasigroup; heterogeneous algebra; hyperidentity; modular group; conjugate; parastrophe; time reversal
Summary:
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 $2n$ 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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