{
  "id": "1804.00692",
  "version": "v1",
  "published": "2018-04-02T18:46:35.000Z",
  "updated": "2018-04-02T18:46:35.000Z",
  "title": "The generators of $3$-class group of some fields of degree $6$ over $\\mathbb{Q}$",
  "authors": [
    "Siham Aouissi",
    "Moulay Chrif Ismaili",
    "Mohamed Talbi",
    "Abdelmalek Azizi"
  ],
  "comment": "16 pages, 2 tables",
  "journal": "Boletim Sociedade Paranaense de Mathematica Journal 2018",
  "doi": "10.5269/bspm.40672",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $\\mathrm{k}=\\mathbb{Q}\\left(\\sqrt[3]{p},\\zeta_3\\right)$, where $p$ is a prime number such that $p \\equiv 1 \\pmod 9$, and let $C_{\\mathrm{k},3}$ be the $3$-component of the class group of $\\mathrm{k}$. In \\cite{GERTH3}, Frank Gerth III proves a conjecture made by Calegari and Emerton \\cite{Cal-Emer} which gives necessary and sufficient conditions for $C_{\\mathrm{k},3}$ to be of $\\operatorname{rank}\\,$ two. The purpose of the present work is to determine generators of $C_{\\mathrm{k},3}$, whenever it is isomorphic to $\\mathbb{Z}/9\\mathbb{Z} \\times \\mathbb{Z}/3\\mathbb{Z}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-04-02T18:46:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R11",
      "11R16",
      "11R20",
      "11R27",
      "11R29",
      "11R37"
    ],
    "keywords": [
      "class group",
      "prime number",
      "frank gerth",
      "sufficient conditions",
      "determine generators"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}