{
  "id": "1312.0251",
  "version": "v1",
  "published": "2013-12-01T17:25:32.000Z",
  "updated": "2013-12-01T17:25:32.000Z",
  "title": "$3$-class field towers of exact length $3$",
  "authors": [
    "MIchael R. Bush",
    "Daniel C. Mayer"
  ],
  "comment": "8 pages",
  "categories": [
    "math.NT",
    "math.GR"
  ],
  "abstract": "The $p$-group generation algorithm is used to verify that the Hilbert $3$-class field tower has length $3$ for certain imaginary quadratic fields $K$ with $3$-class group $\\mathrm{Cl}_3(K) \\cong [3,3]$. Our results provide the first examples of finite $p$-class towers of length $> 2$ for an odd prime $p$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-12-01T17:25:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R37",
      "11R11",
      "11R29",
      "20D15",
      "20F14"
    ],
    "keywords": [
      "class field tower",
      "exact length",
      "imaginary quadratic fields",
      "group generation algorithm",
      "class group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1312.0251B"
    }
  }
}