{
  "id": "1206.6160",
  "version": "v6",
  "published": "2012-06-27T02:57:32.000Z",
  "updated": "2012-08-21T05:33:15.000Z",
  "title": "Restricted Sumsets in Finite Nilpotent Groups",
  "authors": [
    "Shanshan Du",
    "Hao Pan"
  ],
  "comment": "This is a preliminary draft, which maybe contains some mistakes. Now Theorem 1.2 has been extended to general finite groups",
  "categories": [
    "math.CO",
    "math.GR",
    "math.NT"
  ],
  "abstract": "Suppose that $A,B$ are two non-empty subsets of the finite nilpotent group $G$. If $A\\not=B$, then the cardinality of the restricted sumset $$A\\dotplus B={a+b: a\\in A, b\\in B, a\\neq b} $$ is at least $$\\min{p(G),|A|+|B|-2},$$ where $p(G)$ denotes the least prime factor of $|G|$.",
  "revisions": [
    {
      "version": "v6",
      "updated": "2012-08-21T05:33:15.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite nilpotent group",
      "restricted sumset",
      "non-empty subsets",
      "prime factor"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1206.6160D"
    }
  }
}