{
  "id": "1112.1522",
  "version": "v2",
  "published": "2011-12-07T11:04:05.000Z",
  "updated": "2012-01-05T10:32:28.000Z",
  "title": "On realizability of $p$-groups as Galois groups",
  "authors": [
    "Ivo M. Michailov",
    "Nikola P. Ziapkov"
  ],
  "comment": "In this version is added an example at the end of Section 6. Also, some mistakes are corrected and the references are updated",
  "categories": [
    "math.AG"
  ],
  "abstract": "In this article we survey and examine the realizability of $p$-groups as Galois groups over arbitrary fields. In particular we consider various cohomological criteria that lead to necessary and sufficient conditions for the realizability of such a group as a Galois group, the embedding problem (i.e., realizability over a given subextension), descriptions of such extensions, automatic realizations among $p$-groups, and related topics.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-01-05T10:32:28.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "galois group",
      "realizability",
      "arbitrary fields",
      "sufficient conditions",
      "automatic realizations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1112.1522M"
    }
  }
}