{
  "id": "2006.05523",
  "version": "v1",
  "published": "2020-06-09T21:42:11.000Z",
  "updated": "2020-06-09T21:42:11.000Z",
  "title": "Invariable generation does not pass to finite index subgroups",
  "authors": [
    "Gil Goffer",
    "Nir Lazarovich"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "Using small cancellation methods, we show that the property invariable generation does not pass to finite index subgroups, answering questions of Wiegold and Kantor-Lubotzky-Shalev. We further show that a finitely generated group that is invariably generated is not necessarily finitely invariably generated, answering a question of Cox. The same results were also obtained independently by Minasyan.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-06-09T21:42:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F06",
      "20F67",
      "20F65"
    ],
    "keywords": [
      "finite index subgroups",
      "small cancellation methods",
      "property invariable generation",
      "finitely generated group",
      "answering questions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}