{
  "id": "math/0201293",
  "version": "v3",
  "published": "2002-01-30T01:45:44.000Z",
  "updated": "2017-11-23T11:17:40.000Z",
  "title": "Groups of intermediate growth",
  "authors": [
    "Laurent Bartholdi"
  ],
  "comment": "There are substantial mistakes in this article; some of its claims are as yet open",
  "categories": [
    "math.GR"
  ],
  "abstract": "I describe a class of groups acting on rooted trees. The original claim was that all have intermediate word growth between polynomial and exponential. The argument constructs a functional equation on the growth formal power series, and derives the growth properties from its analytical behaviour. Unfortunately, there are substantial mistakes in the proofs, so the main claims should be considered unsettled. In particular, it is still an open problem whether the growth of the Gupta-Sidki group is intermediate or exponential.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2002-07-13T23:10:41.000Z",
      "abstract": "I describe a class of groups acting on rooted trees that all have intermediate word growth between polynomial and exponential. The argument constructs a functional equation on the growth formal power series, and derives the growth properties from its analytical behaviour. This places under a unified proof all known or conjectured examples of such groups, and answers a few open questions by Rostislav Grigorchuk.",
      "comment": "9 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2017-11-23T11:17:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20E08",
      "20F32"
    ],
    "keywords": [
      "intermediate growth",
      "growth formal power series",
      "intermediate word growth",
      "functional equation",
      "argument constructs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math......1293B"
    }
  }
}