{
  "id": "math/0202281",
  "version": "v2",
  "published": "2002-02-26T20:04:27.000Z",
  "updated": "2003-03-08T02:53:14.000Z",
  "title": "Classification of Finite Alexander Quandles",
  "authors": [
    "Sam Nelson"
  ],
  "comment": "10 pages, LaTeX. Typos corrected, proof of Theorem 2.1 fixed. To appear in Topology Proceedings",
  "journal": "Topology Proceedings 27 (2003) pp. 245-258.",
  "categories": [
    "math.GT",
    "math.AT"
  ],
  "abstract": "Two 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.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2003-03-08T02:53:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M27"
    ],
    "keywords": [
      "finite alexander quandles",
      "linear quandles",
      "classification",
      "isomorphic",
      "yields specific conditions"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math......2281N"
    }
  }
}