{
  "id": "1212.0595",
  "version": "v1",
  "published": "2012-12-04T01:26:02.000Z",
  "updated": "2012-12-04T01:26:02.000Z",
  "title": "On The Critical Number of Finite Groups (II)",
  "authors": [
    "Qinghong Wang",
    "Yongke Qu"
  ],
  "categories": [
    "math.NT",
    "math.CO"
  ],
  "abstract": "Let G be a finite group and S a subset of G\\{0}. We call S an additive basis of G if every element of G can be expressed as a sum over a nonempty subset in some order. Let cr(G) be the smallest integer t such that every subset of G\\{0} of cardinality t is an additive basis of G. In this paper, we determine cr(G) for the following cases: (i) G is a finite nilpotent group; (ii) G is a group of even order which possesses a subgroup of index 2.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-12-04T01:26:02.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite group",
      "critical number",
      "additive basis",
      "finite nilpotent group",
      "nonempty subset"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1212.0595W"
    }
  }
}