{
  "id": "2012.10417",
  "version": "v1",
  "published": "2020-12-18T18:14:30.000Z",
  "updated": "2020-12-18T18:14:30.000Z",
  "title": "Algorithmic problems in groups with quadratic Dehn function",
  "authors": [
    "A. Yu. Olshanskii",
    "M. V. Sapir"
  ],
  "comment": "45 pages. arXiv admin note: text overlap with arXiv:1809.00280",
  "categories": [
    "math.GR"
  ],
  "abstract": "We construct and study finitely presented groups with quadratic Dehn function (QD-groups) and present the following applications of the method developed in our recent papers. (1) The isomorphism problem is undecidable in the class of QD-groups. (2) For every recursive function $f$, there is a QD-group $G$ containing a finitely presented subgroup $H$ whose Dehn function grows faster than $f$. (3) There exists a group with undecidable conjugacy problem but decidable power conjugacy problem; this group is QD.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-12-18T18:14:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F05",
      "20F06",
      "20F65",
      "03D10"
    ],
    "keywords": [
      "quadratic dehn function",
      "algorithmic problems",
      "dehn function grows faster",
      "decidable power conjugacy problem",
      "undecidable conjugacy problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 45,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}