{
  "id": "1409.0125",
  "version": "v1",
  "published": "2014-08-30T15:34:36.000Z",
  "updated": "2014-08-30T15:34:36.000Z",
  "title": "On finite generation of self-similar groups of finite type",
  "authors": [
    "Ievgen V. Bondarenko",
    "Igor O. Samoilovych"
  ],
  "comment": "11 pages",
  "journal": "IJAC, Volume 23, Number 1, 69-79, 2013",
  "categories": [
    "math.GR"
  ],
  "abstract": "A self-similar group of finite type is the profinite group of all automorphisms of a regular rooted tree that locally around every vertex act as elements of a given finite group of allowed actions. We provide criteria for determining when a self-similar group of finite type is finite, level-transitive, or topologically finitely generated. Using these criteria and GAP computations we show that for the binary alphabet there is no infinite topologically finitely generated self-similar group given by patterns of depth $3$, and there are $32$ such groups for depth $4$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-08-30T15:34:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F65",
      "20F05",
      "20E08"
    ],
    "keywords": [
      "finite type",
      "finite generation",
      "finitely generated self-similar group",
      "vertex act",
      "infinite topologically finitely generated self-similar"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}