{
  "id": "2305.06184",
  "version": "v1",
  "published": "2023-05-10T14:15:58.000Z",
  "updated": "2023-05-10T14:15:58.000Z",
  "title": "Groups with anticentral elements",
  "authors": [
    "Frieder Ladisch"
  ],
  "comment": "12 pages; old paper from 2008 put on arXiv for the sake of \"green\" open access",
  "journal": "Comm. Algebra 36, no. 8 (2008), pp 2883-2894",
  "doi": "10.1080/00927870802108106",
  "categories": [
    "math.GR"
  ],
  "abstract": "We study finite groups $G$ with elements $g$ such that $\\lvert \\mathbf{C}_G(g)\\rvert = \\lvert G:G' \\rvert$. (Such elements generalize fixed-point-free automorphisms of finite groups.) We show that these groups have a unique conjugacy class of nilpotent supplements for the commutator subgroup and, using the classification of finite simple groups, that these groups are solvable.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-05-10T14:15:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20D10",
      "20D15",
      "20C15"
    ],
    "keywords": [
      "anticentral elements",
      "finite simple groups",
      "study finite groups",
      "elements generalize fixed-point-free automorphisms",
      "unique conjugacy class"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Taylor-Francis"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}