{
  "id": "math/0508247",
  "version": "v3",
  "published": "2005-08-14T20:57:41.000Z",
  "updated": "2006-06-14T21:36:55.000Z",
  "title": "On the Orbit Decomposition of Finite Quandles",
  "authors": [
    "Sam Nelson",
    "Chau-Yim Wong"
  ],
  "comment": "Version 3 includes changes suggested by referee. To appear in JKTR",
  "journal": "J. Knot Theory Ramifications 15 (2006) 761-772.",
  "categories": [
    "math.GT"
  ],
  "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.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2006-06-14T21:36:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M27",
      "57M25"
    ],
    "keywords": [
      "finite quandle",
      "usual orbit decomposition",
      "non-connected quandle structures",
      "structure maps",
      "natural way"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......8247N"
    }
  }
}