{
  "id": "0803.3805",
  "version": "v1",
  "published": "2008-03-26T20:06:17.000Z",
  "updated": "2008-03-26T20:06:17.000Z",
  "title": "Largeness of LERF and 1-relator groups",
  "authors": [
    "Jack Button"
  ],
  "comment": "33 pages; contains a problem list on pages 22 to 28",
  "categories": [
    "math.GR"
  ],
  "abstract": "We consider largeness of groups given by a presentation of deficiency 1, where the group is respectively free-by-cyclic, LERF or 1-relator. We give the first examples of (finitely generated free)-by-(infinite cyclic) word hyperbolic groups which are large, show that a LERF deficiency 1 group with first Betti number at least 2 is large or the integers times the integers, and show that 2-generator 1-relator groups where the relator has height 1 obey the dichotomy that either the group is large or all its finite images are metacyclic.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-03-26T20:06:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F05"
    ],
    "keywords": [
      "word hyperbolic groups",
      "first betti number",
      "finite images",
      "first examples",
      "lerf deficiency"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0803.3805B"
    }
  }
}