{
  "id": "2406.00797",
  "version": "v1",
  "published": "2024-06-02T16:43:20.000Z",
  "updated": "2024-06-02T16:43:20.000Z",
  "title": "Infinite class field tower with small root discriminant",
  "authors": [
    "Zugan Xing",
    "Qi Liu"
  ],
  "comment": "7 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We extend Schoof's theorem from cyclic case to any finite case and apply this to construct a class of $\\mathbb Z/m\\mathbb Z \\rtimes \\mathbb Z/\\varphi(n)\\mathbb Z$ extensions of $\\mathbb Q$, where $m$ is either a power of $2$ or an odd integer, and $n$ be any integer such that $m$ divides $n$. As an application, we give some number fields with small root discriminant, having infinite $p$-class field tower when $p=3, 5, 7$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-06-02T16:43:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R29",
      "11R37"
    ],
    "keywords": [
      "infinite class field tower",
      "small root discriminant",
      "extend schoofs theorem",
      "number fields",
      "odd integer"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}