{
  "id": "2002.00648",
  "version": "v1",
  "published": "2020-02-03T11:19:58.000Z",
  "updated": "2020-02-03T11:19:58.000Z",
  "title": "On element orders in covers of $L_4(q)$ and $U_4(q)$",
  "authors": [
    "Mariya A. Grechkoseeva",
    "Saveliy V. Skresanov"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "Suppose that $L$ is one of the finite simple groups $PSL_4(q)$ or $PSU_4(q)$ and $L$ acts on a vector space $W$ over a field whose characteristic divides $q$. We prove that the natural semidirect product of $W$ and $L$ contains an element whose order differs from the order of any element of $L$, thus answering questions 14.60 and 17.73 (a) of the Kourovka Notebook.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-02-03T11:19:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20D06",
      "20D60",
      "20C20"
    ],
    "keywords": [
      "element orders",
      "finite simple groups",
      "natural semidirect product",
      "characteristic divides",
      "kourovka notebook"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}