Classification of Finite Alexander Quandles

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dc.creatorNelson, Sam
dc.date2002-02-26
dc.date2003-03-08
dc.date.accessioned2026-07-07T06:22:34Z
dc.date.available2026-07-07T06:22:34Z
dc.descriptionTwo finite Alexander quandles with the same number of elements are isomorphic iff their Z[t,t^-1]-submodules Im(1-t) are isomorphic as modules. This yields specific conditions on when Alexander quandles of the form Z_n[t,t^-1]/(t-a) where gcd(n,a)=1 (called linear quandles) are isomorphic, as well as specific conditions on when two linear quandles are dual and which linear quandles are connected. We apply this result to obtain a procedure for classifying Alexander quandles of any finite order and as an application we list the numbers of distinct and connected Alexander quandles with up to fifteen elements.
dc.description10 pages, LaTeX. Typos corrected, proof of Theorem 2.1 fixed. To appear in Topology Proceedings
dc.identifierhttps://arxiv.org/abs/math/0202281
dc.identifierhttp://arxiv.org/abs/math/0202281
dc.identifierTopology Proceedings 27 (2003) pp. 245-258.
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/95947
dc.subjectGeometric Topology
dc.subjectAlgebraic Topology
dc.subject57M27
dc.titleClassification of Finite Alexander Quandles
dc.typetext

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