{
  "id": "1107.1826",
  "version": "v3",
  "published": "2011-07-10T00:09:30.000Z",
  "updated": "2015-01-27T18:23:03.000Z",
  "title": "Conjugacy growth of finitely generated groups",
  "authors": [
    "M. Hull",
    "D. Osin"
  ],
  "comment": "The published version of this paper contained an inaccuracy in the proof of Corollary 5.6, which is corrected in this version",
  "journal": "Adv. Math. 235 (2013), 361-389",
  "categories": [
    "math.GR",
    "math.GT"
  ],
  "abstract": "We show that every non-decreasing function $f\\colon \\mathbb N\\to \\mathbb N$ bounded from above by $a^n$ for some $a\\ge 1$ can be realized (up to a natural equivalence) as the conjugacy growth function of a finitely generated group. We also construct a finitely generated group $G$ and a subgroup $H\\le G$ of index 2 such that $H$ has only 2 conjugacy classes while the conjugacy growth of $G$ is exponential. In particular, conjugacy growth is not a quasi-isometry invariant.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-12-03T01:52:32.000Z",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2015-01-27T18:23:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F69",
      "20E45",
      "20F65",
      "20F67"
    ],
    "keywords": [
      "finitely generated group",
      "conjugacy growth function",
      "quasi-isometry invariant",
      "conjugacy classes",
      "natural equivalence"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Elsevier",
      "journal": "Adv. Math."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1107.1826H"
    }
  }
}