{
  "id": "1403.8132",
  "version": "v2",
  "published": "2014-03-31T19:14:53.000Z",
  "updated": "2018-01-31T17:08:04.000Z",
  "title": "On normal subgroups of the braided Thompson groups",
  "authors": [
    "Matthew C. B. Zaremsky"
  ],
  "comment": "21 pages, 6 figures. v2: accepted version, to appear in Groups, Geometry & Dynamics",
  "categories": [
    "math.GR"
  ],
  "abstract": "We inspect the normal subgroup structure of the braided Thompson groups Vbr and Fbr. We prove that every proper normal subgroup of Vbr lies in the kernel of the natural quotient Vbr \\onto V, and we exhibit some families of interesting such normal subgroups. For Fbr, we prove that for any normal subgroup N of Fbr, either N is contained in the kernel of Fbr \\onto F, or else N contains [Fbr,Fbr]. We also compute the Bieri-Neumann-Strebel invariant Sigma^1(Fbr), which is a useful tool for understanding normal subgroups containing the commutator subgroup.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-03-31T19:14:53.000Z",
      "comment": "21 pages, 6 figures",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2018-01-31T17:08:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F65"
    ],
    "keywords": [
      "normal subgroup structure",
      "braided thompson groups vbr",
      "proper normal subgroup",
      "natural quotient vbr",
      "bieri-neumann-strebel invariant"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1403.8132Z"
    }
  }
}