{
  "id": "1901.04348",
  "version": "v1",
  "published": "2019-01-14T14:35:20.000Z",
  "updated": "2019-01-14T14:35:20.000Z",
  "title": "Groupoids and the algebra of rewriting in group presentations",
  "authors": [
    "N. D. Gilbert",
    "E. A. McDougall"
  ],
  "comment": "15 pages",
  "categories": [
    "math.GR"
  ],
  "abstract": "Presentations of groups by rewriting systems (that is, by monoid presentations), have been fruitfully studied by encoding the rewriting system in a $2$--complex -- the Squier complex -- whose fundamental groupoid then describes the derivation of consequences of the rewrite rules. We describe a reduced form of the Squier complex, investigate the structure of its fundamental groupoid, and show that key properties of the presentation are still encoded in the reduced form.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-01-14T14:35:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F05"
    ],
    "keywords": [
      "group presentations",
      "squier complex",
      "fundamental groupoid",
      "rewriting system",
      "reduced form"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}