Toward a classification of finite quandles

Details Toward a classification of finite quandles Toward a classification of finite quandles

2005-12-06

arxiv.org/abs/math/0512135v1

Mathematics

Quantum Algebra

12 pages LaTeX

Scientific paper

This paper summarizes substantive new results derived by a student team (the first three authors) under the direction of the fourth author at the 2005 session of the KSU REU ``Brainstorming and Barnstorming''. The main results are a decomposition theorem for quandles in terms of an operation of `semidisjoint union' showing that all finite quandles canonically decompose via iterated semidisjoint unions into connected subquandles, and a structure theorem for finite connected quandles with prescribe inner automorphism group. The latter theorem suggests a new approach to the classification of finite connected quandles.

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