{
  "id": "1703.07241",
  "version": "v1",
  "published": "2017-03-21T14:36:23.000Z",
  "updated": "2017-03-21T14:36:23.000Z",
  "title": "A remark On Abelianized Absolute Galois Group of Imaginary Quadratic Fields",
  "authors": [
    "Bart de Smit",
    "Pavel Solomatin"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:1703.05729",
  "categories": [
    "math.NT"
  ],
  "abstract": "The main purpose of this paper is to extend results on isomorphism types of the abelianized absolute Galois group $\\mathcal G_K^{ab}$, where $K$ denotes imaginary quadratic field. In particular, we will show that if the class number $h_K$ of an imaginary quadratic field $K$ different from $\\mathbb Q(i)$, $\\mathbb Q(\\sqrt{-2})$ is a fixed prime number $p$ then there are only two isomorphism types of $\\mathcal G_K^{ab}$ which could occur. For instance, this result implies that imaginary quadratic fields of the discriminant $D_K$ belonging to the set $\\{-35, -51, -91, -115, -123, -187, -235,$ $ -267,-403, -427 \\}$ all have isomorphic abelian parts of their absolute Galois groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-03-21T14:36:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "abelianized absolute galois group",
      "denotes imaginary quadratic field",
      "isomorphism types",
      "isomorphic abelian parts",
      "fixed prime number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}