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ON THE ORBIT DECOMPOSITION OF FINITE QUANDLES

SAM NELSON

Department of Mathematics, University of California, Riverside, 900 University Avenue, Riverside, CA 92521, USA

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and

CHAU-YIM WONG

Department of Mathematics, University of California, Riverside, 900 University Avenue, Riverside, CA 92521, USA

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https://doi.org/10.1142/S0218216506004701Cited by:20 (Source: Crossref)

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 an algorithm for finding quandle structures on a disjoint union of quandles.

Keywords:

AMSC: 57M25, 57M27

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