{
  "id": "2407.19554",
  "version": "v1",
  "published": "2024-07-28T18:21:40.000Z",
  "updated": "2024-07-28T18:21:40.000Z",
  "title": "On the average size of $3$-torsion in class groups of $C_2 \\wr H$-extensions",
  "authors": [
    "Jonas Iskander",
    "Hari Iyer"
  ],
  "comment": "6 pages, 0 figures",
  "categories": [
    "math.NT",
    "math.GR"
  ],
  "abstract": "The Cohen-Lenstra-Martinet heuristics lead one to conjecture that the average size of the $p$-torsion in class groups of $G$-extensions of a number field is finite. In a 2021 paper, Lemke Oliver, Wang, and Wood proved this conjecture in the case of $p = 3$ for permutation groups $G$ of the form $C_2 \\wr H$ for a broad family of permutation groups $H$, including most nilpotent groups. However, their theorem does not apply for some nilpotent groups of interest, such as $H = C_5$. We extend their results to prove that the average size of $3$-torsion in class groups of $C_2 \\wr H$-extensions is finite for any nilpotent group $H$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-07-28T18:21:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R29"
    ],
    "keywords": [
      "class groups",
      "average size",
      "extensions",
      "nilpotent group",
      "permutation groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}