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arXiv · 2104.10199

A Sufficient Condition for a Quandle to be Latin

António Lages·Pedro Lopes·Petr Vojtěchovský
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Abstract

A quandle is an algebraic structure satisfying three axioms: idempotency, right-invertibility and right self-distributivity. In quandles, right translations are permutations. The profile of a quandle is the list of cycle structures, one per right translation in the quandle. In this note we prove that if, for each cycle structure in the profile of a quandle, no two cycle lengths are equal, then the quandle is latin -- this is the sufficient condition mentioned in the title.

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António Lages, Pedro Lopes, Petr Vojtěchovský. 2021-12-09. A Sufficient Condition for a Quandle to be Latin. https://arxiv.org/abs/2104.10199

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