{
  "id": "1410.5271",
  "version": "v1",
  "published": "2014-10-20T13:41:41.000Z",
  "updated": "2014-10-20T13:41:41.000Z",
  "title": "Invariable generation of prosoluble groups",
  "authors": [
    "Eloisa Detomi",
    "Andrea Lucchini"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "A group $G$ is invariably generated by a subset $S$ of $G$ if $G= s^{g(s)} \\mid s\\in S$ for each choice of $g(s) \\in G$, $s \\in S$. Answering two questions posed by Kantor, Lubotzky and Shalev, we prove that the free prosoluble group of rank $d \\ge 2$ can not be invariably generated by a finite set of elements, while the free solvable profinite group of rank $d$ and derived length $l$ is invariably generated by precisely $l(d-1)+1$ elements.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-10-20T13:41:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "invariable generation",
      "invariably",
      "free solvable profinite group",
      "free prosoluble group",
      "finite set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1410.5271D"
    }
  }
}