{
  "id": "2002.01446",
  "version": "v1",
  "published": "2020-02-04T18:16:02.000Z",
  "updated": "2020-02-04T18:16:02.000Z",
  "title": "Twisted conjugacy classes in twisted Chevalley groups",
  "authors": [
    "Sushil Bhunia",
    "Pinka Dey",
    "Amit Roy"
  ],
  "comment": "15 pages. All comments are welcome",
  "categories": [
    "math.GR"
  ],
  "abstract": "Let G be a group and {\\phi} be an automorphism of G. Two elements x, y of G are said to be {\\phi}-twisted if y = gx{\\phi}(g)^{-1} for some g in G. We say that a group G has the R_{\\infty}-property if the number of {\\phi}-twisted conjugacy classes is infinite for every automorphism {\\phi} of G. In this paper, we prove that twisted Chevalley groups over the field k of characteristic zero have the R_{\\infty}-property as well as S_{\\infty}-property if k has finite transcendence degree over \\mathbb{Q} or Aut(k) is periodic.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-02-04T18:16:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20E45"
    ],
    "keywords": [
      "twisted chevalley groups",
      "twisted conjugacy classes",
      "finite transcendence degree",
      "automorphism",
      "characteristic zero"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}