On the Orbit Decomposition of Finite Quandles

Sam Nelson; Chau-Yim Wong

On the Orbit Decomposition of Finite Quandles

Geometric Topology 2007-05-23 v3

Authors: Sam Nelson , Chau-Yim Wong

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.

Keywords

finite quandles subquandles orbit decomposition q-complemented non-connected quandles

Cite

@article{arxiv.math/0508247,
  title  = {On the Orbit Decomposition of Finite Quandles},
  author = {Sam Nelson and Chau-Yim Wong},
  journal= {arXiv preprint arXiv:math/0508247},
  year   = {2007}
}

Comments

Version 3 includes changes suggested by referee. To appear in JKTR

On the Orbit Decomposition of Finite Quandles

Abstract

Keywords

Cite

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