{
  "id": "1401.2790",
  "version": "v1",
  "published": "2014-01-13T11:26:56.000Z",
  "updated": "2014-01-13T11:26:56.000Z",
  "title": "The isomorphism problem for profinite completions of residually finite groups",
  "authors": [
    "Martin R. Bridson",
    "Henry Wilton"
  ],
  "comment": "12 pages",
  "categories": [
    "math.GR",
    "math.GT"
  ],
  "abstract": "We consider pairs of finitely presented, residually finite groups $u:P\\hookrightarrow \\Gamma$. We prove that there is no algorithm that, given an arbitrary such pair, can determine whether or not the associated map of profinite completions $\\hat{u}: \\widehat{P} \\to \\widehat{\\Gamma}$ is an isomorphism. Nor do there exist algorithms that can decide whether $\\hat{u}$ is surjective, or whether $\\widehat{P}$ is isomorphic to $\\widehat{\\Gamma}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-01-13T11:26:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20E18",
      "20F10",
      "57M07",
      "20F65"
    ],
    "keywords": [
      "residually finite groups",
      "profinite completions",
      "isomorphism problem",
      "associated map"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1401.2790B"
    }
  }
}