{
  "id": "1704.03897",
  "version": "v1",
  "published": "2017-04-12T18:49:33.000Z",
  "updated": "2017-04-12T18:49:33.000Z",
  "title": "Commutators of Welded Braid Groups",
  "authors": [
    "Soumya Dey",
    "Krishnendu Gongopadhyay"
  ],
  "comment": "15 pages",
  "categories": [
    "math.GT",
    "math.GR"
  ],
  "abstract": "We investigate commutator subgroups of some generalized braid groups. Let $WB_n'$ be the commutator subgroup of welded (or loop) braid group on n strands. We prove that $WB_n'$ is Hopfian and for $n \\geq 5$, it is perfect. We compute finite presentations for commutator subgroups of flat virtual and flat welded braid groups. We also investigate adorability of these groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-04-12T18:49:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F36",
      "20F12"
    ],
    "keywords": [
      "commutator subgroup",
      "flat welded braid groups",
      "generalized braid groups",
      "finite presentations",
      "flat virtual"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}