{
  "id": "math/9809108",
  "version": "v1",
  "published": "1998-09-19T04:10:59.000Z",
  "updated": "1998-09-19T04:10:59.000Z",
  "title": "Quasi-isometric rigidity for PSL(2,Z[1/p])",
  "authors": [
    "Jennifer Taback"
  ],
  "comment": "29 pages, 4 figures, LaTeX, epsfig",
  "categories": [
    "math.GR",
    "math.GT"
  ],
  "abstract": "We prove that PSL(2,Z[1/p]) gives the first example of groups which are not quasi-isometric to each other but have the same quasi-isometry group. Namely, PSL(2,Z[1/p]) and PSL(2,Z[1/q]) are not quasi-isometric unless p=q, and, independent of p, the quasi-isometry group of PSL(2,Z[1/p]) is PSL(2,Q). In addition, we characterize PSL(2,Z[1/p]) uniquely among all finitely generated groups by its quasi-isometry type.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1998-09-19T04:10:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F32"
    ],
    "keywords": [
      "quasi-isometric rigidity",
      "quasi-isometry group",
      "first example",
      "quasi-isometry type"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1998math......9108T"
    }
  }
}