{
  "id": "1908.01982",
  "version": "v1",
  "published": "2019-08-06T06:54:14.000Z",
  "updated": "2019-08-06T06:54:14.000Z",
  "title": "Harmonically balanced capitulation over quadratic fields of type (9,9)",
  "authors": [
    "Daniel C. Mayer"
  ],
  "comment": "13 pages, 4 figures, 2 tables",
  "categories": [
    "math.NT",
    "math.GR"
  ],
  "abstract": "The isomorphism type of the Galois group G of finite 3-class field towers of quadratic number fields with 3-class group of type (9,9) is determined by means of Artin patterns which contain information on the transfer of 3-classes to unramified abelian 3-extensions. First, as an approximation of the group G, its metabelianization M=G/G\", which is isomorphic to the Galois group of the second Hilbert 3-class field, is sought by sifting the SmallGroups library with the aid of pattern recognition. In cases with order |M|>3^8, the SmallGroups database must be extended by means of the p-group generation algorithm, which reveals new phenomena of groups with harmonically balanced transfer kernels and trees with periodic trifurcations. Bounds for the relation rank d2(M) of M in dependence on the signature of the quadratic base field admit the decision whether the derived length of G is dl(G)=2 or dl(G)>=3.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-08-06T06:54:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R37",
      "11R11",
      "11R29",
      "11Y40",
      "20D15",
      "20-04"
    ],
    "keywords": [
      "harmonically balanced capitulation",
      "quadratic fields",
      "galois group",
      "quadratic base field admit",
      "p-group generation algorithm"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}