{
  "id": "1611.07177",
  "version": "v1",
  "published": "2016-11-22T07:41:05.000Z",
  "updated": "2016-11-22T07:41:05.000Z",
  "title": "Branch groups and new types of subgroup growth for pro-$p$ groups",
  "authors": [
    "Yiftach Barnea",
    "Jan-Christoph Schlage-Puchta"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "We show that there are uncountably many different growth types for the subgroup growth of pro-$p$ groups, thus, answering one of the main open problems in the theory of subgroup growth. As a by product we show that a class of pro-$p$ branch groups including the Grigorchuk group and the Gupta-Sidki groups have all subgroup growth type $n^{\\log n}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-11-22T07:41:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20E07",
      "20E08",
      "20E18"
    ],
    "keywords": [
      "branch groups",
      "main open problems",
      "subgroup growth type",
      "grigorchuk group",
      "gupta-sidki groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}