{
  "id": "1005.1820",
  "version": "v2",
  "published": "2010-05-11T12:56:08.000Z",
  "updated": "2012-11-23T14:14:37.000Z",
  "title": "Powers of sets in free groups",
  "authors": [
    "Stanislav Safin"
  ],
  "comment": "3 pages",
  "categories": [
    "math.GR"
  ],
  "abstract": "We prove that |A^n| > c_n |A|^{[\\frac{n+1}{2}]} for any finite subset A of a free group if A contains at least two noncommuting elements, where c_n>0 are constants not depending on A. Simple examples show that the order of these estimates are the best possible for each n>0.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-11-23T14:14:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20E05"
    ],
    "keywords": [
      "free group",
      "finite subset",
      "simple examples",
      "noncommuting elements"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1070/SM2011v202n11ABEH004203",
      "journal": "Sbornik: Mathematics",
      "year": 2011,
      "month": "Nov",
      "volume": 202,
      "number": 11,
      "pages": 1661
    },
    "note": {
      "typesetting": "TeX",
      "pages": 3,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011SbMat.202.1661S"
    }
  }
}