{
  "id": "math/0110343",
  "version": "v1",
  "published": "2001-10-24T00:00:00.000Z",
  "updated": "2001-10-24T00:00:00.000Z",
  "title": "Computation of Galois groups associated to the 2-class towers of some quadratic fields",
  "authors": [
    "Michael R. Bush"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "The $p$-group generation algorithm from computational group theory is used to obtain information about large quotients of the pro-2 group $G = \\text{Gal} (k^{nr,2}/k)$ for $k = \\mathbb{Q}(\\sqrt{d})$ with $d = -445, -1015, -1595, -2379$. In each case we are able to narrow the identity of $G$ down to one of a finite number of explicitly given finite groups. From this follow several results regarding the corresponding 2-class tower. This is a revised version of ANT-0302.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2001-10-24T00:00:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "galois groups",
      "quadratic fields",
      "computational group theory",
      "group generation algorithm",
      "large quotients"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001math.....10343B"
    }
  }
}