{
  "id": "1312.4998",
  "version": "v1",
  "published": "2013-12-17T23:13:14.000Z",
  "updated": "2013-12-17T23:13:14.000Z",
  "title": "A Refined Waring Problem for Finite Simple Groups",
  "authors": [
    "Michael Larsen",
    "Pham Huu Tiep"
  ],
  "comment": "20 pages",
  "categories": [
    "math.GR"
  ],
  "abstract": "Let v and w be nontrivial words in two free groups. We prove that, for all sufficiently large finite non-abelian simple groups G, there exist subsets C of v(G) and D of w(G) of size such that every element of G can be realized in at least one way as the product of an element of C and an element of D and the average number of such representations is O(log |G|). In particular, if w is a fixed nontrivial word and G is a sufficiently large finite non-abelian simple group, then w(G) contains a thin base of order 2. This is a non-abelian analogue of a result of Van Vu for the classical Waring problem. Further results concerning thin bases of G of order 2 are established for any finite group and for any compact Lie group G.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-12-17T23:13:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20D06",
      "11B13",
      "11P05",
      "20C33",
      "22C05"
    ],
    "keywords": [
      "finite simple groups",
      "refined waring problem",
      "large finite non-abelian simple group",
      "sufficiently large finite non-abelian simple",
      "thin base"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1312.4998L"
    }
  }
}