{
  "id": "1912.08146",
  "version": "v1",
  "published": "2019-12-17T17:25:58.000Z",
  "updated": "2019-12-17T17:25:58.000Z",
  "title": "On nilpotent automorphism groups of function fields",
  "authors": [
    "Nurdagül Anbar",
    "Burçin Güneş"
  ],
  "comment": "14 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "We study the automorphisms of a function field of genus $g\\geq 2$ over an algebraically closed field of characteristic $p>0$. More precisely, we show that the order of a nilpotent subgroup $G$ of its automorphism group is bounded by $16 (g-1)$ when G is not a $p$-group. We show that if $|G|=16(g-1) $, then $g-1$ is a power of $2$. Furthermore, we provide an infinite family of function fields attaining the bound.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-12-17T17:25:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14H05",
      "14H37"
    ],
    "keywords": [
      "nilpotent automorphism groups",
      "nilpotent subgroup",
      "characteristic",
      "algebraically closed field",
      "function fields attaining"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}