{
  "id": "1403.7977",
  "version": "v1",
  "published": "2014-03-31T12:59:02.000Z",
  "updated": "2014-03-31T12:59:02.000Z",
  "title": "Using a Galois connection to compute character degrees",
  "authors": [
    "Mark L. Lewis",
    "John K. McVey"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "Given a Mersenne prime $q$ and a positive even integer $e$, let $F$ and $E$ be the fields of orders $q$ and $q^e$ respectively. Let $C$ be a cyclic subgroup of $E^\\times$ whose index in $E^\\times$ is divisible only by primes dividing $q - 1$. We compute the character degrees of the group $C \\rtimes {\\rm Gal} (E/F)$ by using the Galois connection between the subfields of $E$ and the Galois group ${\\rm Gal} (E/F)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-03-31T12:59:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20C15"
    ],
    "keywords": [
      "character degrees",
      "galois connection",
      "mersenne prime",
      "galois group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1403.7977L"
    }
  }
}