{
  "id": "math/0404075",
  "version": "v1",
  "published": "2004-04-05T05:13:42.000Z",
  "updated": "2004-04-05T05:13:42.000Z",
  "title": "Algebraic entropy of elementary amenable groups",
  "authors": [
    "D. V. Osin"
  ],
  "comment": "20 pages; to appear in Geom. Dedicata",
  "categories": [
    "math.GR"
  ],
  "abstract": "We prove that any finitely generated elementary amenable group of zero (algebraic) entropy contains a nilpotent subgroup of finite index or, equivalently, any finitely generated elementary amenable group of exponential growth is of uniformly exponential growth. We also show that 0 is an accumulation point of the set of entropies of elementary amenable groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-04-05T05:13:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F65",
      "20F69"
    ],
    "keywords": [
      "algebraic entropy",
      "finitely generated elementary amenable group",
      "finite index",
      "nilpotent subgroup",
      "entropy contains"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......4075O"
    }
  }
}