{
  "id": "1910.04838",
  "version": "v1",
  "published": "2019-10-10T20:13:18.000Z",
  "updated": "2019-10-10T20:13:18.000Z",
  "title": "Profinite groups in which centralizers are virtually procyclic",
  "authors": [
    "Pavel Shumyatsky",
    "Pavel Zalesskii"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "The article deals with profinite groups in which centralizers are virtually procyclic. Suppose that G is a profinite group such that the centralizer of every nontrivial element is virtually torsion-free while the centralizer of every element of infinite order is virtually procyclic. We show that G is either virtually pro-p for some prime p or virtually torsion-free procyclic. The same conclusion holds for profinite groups in which the centralizer of every nontrivial element is virtually procyclic; moreover, if G is not pro-p, then G has finite rank.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-10-10T20:13:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20E18"
    ],
    "keywords": [
      "profinite group",
      "virtually procyclic",
      "centralizer",
      "nontrivial element",
      "article deals"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}