{
  "id": "1910.06944",
  "version": "v1",
  "published": "2019-10-15T17:35:38.000Z",
  "updated": "2019-10-15T17:35:38.000Z",
  "title": "The commutator subgroup of the braid group is generated by two elements",
  "authors": [
    "Kevin Kordek"
  ],
  "comment": "8 pages, 1 figure",
  "categories": [
    "math.GT",
    "math.GR"
  ],
  "abstract": "For $n$ at least 7 and $n$ equal to 5, we give generating sets of size 2 for the commutator subgroup of the braid group on $n$ strands. These generating sets are of the smallest possible cardinality. For $n$ equal to 4 or 6, we give generating sets of size three. We also prove that the commutator subgroup of the braid group on 4 strands cannot be generated by fewer than three elements.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-10-15T17:35:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "braid group",
      "commutator subgroup",
      "generating sets"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}