On the Orbit Decomposition of Finite Quandles

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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.