{
  "id": "0809.2408",
  "version": "v4",
  "published": "2008-09-14T17:30:35.000Z",
  "updated": "2010-06-16T11:29:19.000Z",
  "title": "Normal automorphisms of relatively hyperbolic groups",
  "authors": [
    "A. Minasyan",
    "D. Osin"
  ],
  "comment": "Version 4: final (27 pages, 2 figures)",
  "journal": "Trans. Amer. Math. Soc. 362 (2010), no. 11, 6079-6103",
  "categories": [
    "math.GR",
    "math.GT"
  ],
  "abstract": "An automorphism $\\alpha$ of a group $G$ is normal if it fixes every normal subgroup of $G$ setwise. We give an algebraic description of normal automorphisms of relatively hyperbolic groups. In particular, we prove that for any relatively hyperbolic group $G$, $Inn(G)$ has finite index in the subgroup $Aut_n(G)$ of normal automorphisms. If, in addition, $G$ is non-elementary and has no non-trivial finite normal subgroups, then $Aut_n(G)=Inn(G)$. As an application, we show that $Out(G)$ is residually finite for every finitely generated residually finite group $G$ with more than one end.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2010-06-16T11:29:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F65",
      "20F67",
      "20E26"
    ],
    "keywords": [
      "relatively hyperbolic group",
      "normal automorphisms",
      "non-trivial finite normal subgroups",
      "finitely generated residually finite group",
      "algebraic description"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AMS",
      "journal": "Trans. Amer. Math. Soc."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0809.2408M"
    }
  }
}