{
  "id": "2006.10295",
  "version": "v1",
  "published": "2020-06-18T06:20:03.000Z",
  "updated": "2020-06-18T06:20:03.000Z",
  "title": "Pointwise Bound for $\\ell$-torsion in Class Groups II: Nilpotent Extensions",
  "authors": [
    "Jiuya Wang"
  ],
  "categories": [
    "math.NT",
    "math.GR"
  ],
  "abstract": "For every finite $p$-group $G_p$ that is non-cyclic and non-quaternion and every positive integer $\\ell\\neq p$ that is greater than $2$, we prove the first non-trivial bound on $\\ell$-torsion in class group of every $G_p$-extension. More generally, for every nilpotent group $G$ where every Sylow-$p$ subgroup $G_p\\subset G$ is non-cyclic and non-quaternion, we prove a non-trivial bound on $\\ell$-torsion in class group of every $G$-extension for every integer $\\ell>1$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-06-18T06:20:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R29",
      "20D15"
    ],
    "keywords": [
      "class group",
      "nilpotent extensions",
      "pointwise bound",
      "first non-trivial bound",
      "non-cyclic"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}