{
  "id": "0906.4891",
  "version": "v1",
  "published": "2009-06-26T09:56:14.000Z",
  "updated": "2009-06-26T09:56:14.000Z",
  "title": "On a characterization of locally finite groups in terms of linear cellular automata",
  "authors": [
    "Tullio Ceccherini-Silberstein",
    "Michel Coornaert"
  ],
  "journal": "J. Cell. Autom. 6 (2011), 207-213",
  "categories": [
    "math.GR",
    "math.DS"
  ],
  "abstract": "We prove that a group $G$ is locally finite if and only if every surjective real (or complex) linear cellular automaton with finite-dimensional alphabet over $G$ is injective.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-06-26T09:56:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F50",
      "37B15",
      "68Q80"
    ],
    "keywords": [
      "linear cellular automaton",
      "locally finite groups",
      "characterization",
      "finite-dimensional alphabet"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0906.4891C"
    }
  }
}