On the Orbit Decomposition of Finite Quandles

Sam Nelson; Chau-Yim Wong

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On the Orbit Decomposition of Finite Quandles

Sam Nelson·Chau-Yim Wong

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Abstract

We study the structure of finite quandles in terms of subquandles. Every finite quandle $Q$ decomposes in a natural way as a union of disjoint $Q$-complemented subquandles; this decomposition coincides with the usual orbit decomposition of $Q$. Conversely, the structure of a finite quandle with a given orbit decomposition is determined by its structure maps. We describe a procedure for finding all non-connected quandle structures on a disjoint union of subquandles.

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Sam Nelson, Chau-Yim Wong. 2006-06-14. On the Orbit Decomposition of Finite Quandles. https://arxiv.org/abs/math/0508247

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