{
  "id": "math/0601271",
  "version": "v2",
  "published": "2006-01-12T02:46:37.000Z",
  "updated": "2006-07-22T17:52:54.000Z",
  "title": "Twisted conjugacy and quasi-isometry invariance for generalized solvable Baumslag-Solitar groups",
  "authors": [
    "Jennifer Taback",
    "Peter Wong"
  ],
  "journal": "J. Lond. Math. Soc. (2) 75 (2007), no. 3, 705--717",
  "categories": [
    "math.GR",
    "math.GT"
  ],
  "abstract": "We say that a group has property $R_{\\infty}$ if any group automorphism has an infinite number of twisted conjugacy classes. Fel'shtyn and Goncalves prove that the solvable Baumslag-Solitar groups BS(1,m) have property $R_{\\infty}$. We define a solvable generalization $\\Gamma(S)$ of these groups which we show to have property $R_{\\infty}$. We then show that property $R_{\\infty}$ is geometric for these groups, that is, any group quasi-isometric to $\\Gamma(S)$ has property $R_{\\infty}$ as well.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2006-07-22T17:52:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20E45",
      "20E08",
      "20F65"
    ],
    "keywords": [
      "generalized solvable baumslag-solitar groups",
      "quasi-isometry invariance",
      "solvable baumslag-solitar groups bs",
      "infinite number",
      "twisted conjugacy classes"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......1271T"
    }
  }
}