{
  "id": "1310.6607",
  "version": "v1",
  "published": "2013-10-24T13:24:32.000Z",
  "updated": "2013-10-24T13:24:32.000Z",
  "title": "The 4-class group of real quadratic number fields",
  "authors": [
    "Franz Lemmermeyer"
  ],
  "comment": "unpublished",
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper we give an elementary proof of results on the structure of 4-class groups of real quadratic number fields originally due to A. Scholz. In a second (and independent) section we strengthen C. Maire's result that the 2-class field tower of a real quadratic number field is infinite if its ideal class group has 4-rank at least $4$, using a technique due to F. Hajir.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-10-24T13:24:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R37"
    ],
    "keywords": [
      "real quadratic number fields",
      "ideal class group",
      "maires result",
      "field tower",
      "elementary proof"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1310.6607L"
    }
  }
}