{
  "id": "math/0601359",
  "version": "v1",
  "published": "2006-01-14T17:49:51.000Z",
  "updated": "2006-01-14T17:49:51.000Z",
  "title": "The maximum distinguishing number of a group",
  "authors": [
    "Melody Chan"
  ],
  "comment": "9 pages, to appear in Electronic J. Combinatorics",
  "categories": [
    "math.CO",
    "math.GR"
  ],
  "abstract": "Let G be a group acting faithfully on a set X. The distinguishing number of the action of G on X is the smallest number of colors such that there exists a coloring of X where no nontrivial group element induces a color-preserving permutation of X. In this paper, we show that if G is nilpotent of class c or supersolvable of length c then G always acts with distinguishing number at most c+1. We obtain that all metacyclic groups act with distinguishing number at most 3; these include all groups of squarefree order. We also prove that the distinguishing number of the action of the general linear group over a field K on the vector space K^n is 2 if K has at least n+1 elements.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-01-14T17:49:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E15",
      "20B25",
      "20D60"
    ],
    "keywords": [
      "maximum distinguishing number",
      "nontrivial group element induces",
      "metacyclic groups act",
      "general linear group",
      "smallest number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......1359C"
    }
  }
}