{
  "id": "2005.04314",
  "version": "v1",
  "published": "2020-05-08T23:21:02.000Z",
  "updated": "2020-05-08T23:21:02.000Z",
  "title": "The generators of $5$-class group of some fields of degree 20 over $\\mathbb{Q}$",
  "authors": [
    "Fouad Elmouhib",
    "Mohamed Talbi",
    "Abdelmalek Azizi"
  ],
  "comment": "18 pages, 3 tables",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $\\Gamma \\,=\\, \\mathbb{Q}(\\sqrt[5]{n})$ be a pure quintic field, where $n$ is a positive integer, $5^{th}$ power-free. Let $k_0\\,=\\,\\mathbb{Q}(\\zeta_5)$ be the cyclotomic field containing a primitive $5^{th}$ root of unity $\\zeta_5$, and $k\\,=\\,\\Gamma(\\zeta_5)$ be the normal closure of $\\Gamma$. Let $C_{k,5}$ be the $5$-component of the class group of k. The purpose of this paper is to determine generators of $C_{k,5}$, whenever it is of type $(5,5)$ and the rank of the group of ambiguous classes under the action of $Gal(k/k_0)\\, =\\,\\langle \\sigma\\rangle$ is $1$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-05-08T23:21:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R11",
      "11R16",
      "11R20",
      "11R27",
      "11R29",
      "11R37"
    ],
    "keywords": [
      "class group",
      "pure quintic field",
      "normal closure",
      "determine generators",
      "positive integer"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}