{
  "id": "1309.0133",
  "version": "v1",
  "published": "2013-08-31T16:36:38.000Z",
  "updated": "2013-08-31T16:36:38.000Z",
  "title": "The (7,4)-conjecture in finite groups",
  "authors": [
    "Jozsef Solymosi"
  ],
  "categories": [
    "math.CO",
    "math.GR"
  ],
  "abstract": "The first open case of the Brown, Erd\\H{o}s, S\\'os conjecture is equivalent to the following; For every $c>0$ there is a threshold $n_0$ so that if a quasigroup has order $n\\geq n_0$ then for every subset of triples of the form $(a,b,ab),$ denoted by $S,$ if $|S|\\geq cn^2$ then there is a seven-element subset of the quasigroup which spans at least four triples of the selected subset $S.$ In this paper we prove the conjecture for finite groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-08-31T16:36:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite groups",
      "first open case",
      "seven-element subset",
      "quasigroup",
      "sos conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1309.0133S"
    }
  }
}