{
  "id": "1602.07829",
  "version": "v1",
  "published": "2016-02-25T07:35:56.000Z",
  "updated": "2016-02-25T07:35:56.000Z",
  "title": "The number of composition factors of order $p$ in completely reducible groups of characteristic $p$",
  "authors": [
    "Michael Giudici",
    "S. P. Glasby",
    "Cai Heng Li",
    "Gabriel Verret"
  ],
  "comment": "12 pages",
  "categories": [
    "math.GR"
  ],
  "abstract": "Let $q$ be a power of a prime $p$ and let $G$ be a completely reducible subgroup of $\\mathrm{GL}(d,q)$. We prove that the number of composition factors of $G$ that have prime order $p$ is at most $(\\varepsilon_q d-1)/(p-1)$, where $\\varepsilon_q$ is a function of $q$ satisfying $1\\leqslant\\varepsilon_q\\leqslant 3/2$. For every $q$, we give examples showing this bound is sharp infinitely often.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-02-25T07:35:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20C33",
      "20E34"
    ],
    "keywords": [
      "composition factors",
      "reducible groups",
      "characteristic",
      "prime order"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}