{
  "id": "2110.14834",
  "version": "v2",
  "published": "2021-10-28T01:22:49.000Z",
  "updated": "2022-07-13T14:50:39.000Z",
  "title": "The BNS invariants of the generalized solvable Baumslag-Solitar groups and of their finite index subgroups",
  "authors": [
    "Wagner Sgobbi",
    "Peter Wong"
  ],
  "comment": "20 pages",
  "categories": [
    "math.GR"
  ],
  "abstract": "We compute the Bieri-Neumann-Strebel invariants $\\Sigma^1$ for the generalized solvable Baumslag-Solitar groups $\\Gamma_n$ and their finite index subgroups. Using $\\Sigma^1$, we show that certain finite index subgroups of $\\Gamma_n$ cannot be isomorphic to $\\Gamma_{k}$ for any $k$. In addition, we use the BNS-invariants to give a new proof of property $R_\\infty$ for the groups $\\Gamma_n$ and their finite index subgroups.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2022-07-13T14:50:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F65"
    ],
    "keywords": [
      "finite index subgroups",
      "generalized solvable baumslag-solitar groups",
      "bns invariants",
      "bieri-neumann-strebel invariants",
      "isomorphic"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}