{
  "id": "math/0505198",
  "version": "v2",
  "published": "2005-05-10T21:18:29.000Z",
  "updated": "2006-02-07T00:52:20.000Z",
  "title": "Freiman's Theorem in an arbitrary abelian group",
  "authors": [
    "Ben Green",
    "Imre Z. Ruzsa"
  ],
  "comment": "15 pages, to appear in London Math. Society journals. Exceptionally minor cosmetic changes from the previous version",
  "categories": [
    "math.NT",
    "math.CO"
  ],
  "abstract": "A famous result of Freiman describes the structure of finite sets A of integers with small doubling property. If |A + A| <= K|A| then A is contained within a multidimensional arithmetic progression of dimension d(K) and size f(K)|A|. Here we prove an analogous statement valid for subsets of an arbitrary abelian group.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2006-02-07T00:52:20.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "arbitrary abelian group",
      "freimans theorem",
      "multidimensional arithmetic progression",
      "small doubling property",
      "analogous statement valid"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......5198G"
    }
  }
}