{
  "id": "1703.03834",
  "version": "v1",
  "published": "2017-03-10T20:15:21.000Z",
  "updated": "2017-03-10T20:15:21.000Z",
  "title": "Ramsey-product subsets of a group",
  "authors": [
    "Igor Protasov",
    "Ksenia Protasova"
  ],
  "categories": [
    "math.GN"
  ],
  "abstract": "We say that a subset $S$ of an infinite group $G$ is a Ramsey-product subset if, for any infinite subsets $X$, $Y$ of $G$, there exist $x \\in X$ and $y\\in Y$ such that $x y \\in S$ and $ y x \\in S$ . We show that the family $\\varphi$ of all Ramsey-product subsets of $G$ is a filter and $\\varphi$ defines the subsemigroup $ \\overline{G^*G^*}$ of the semigroup $G^*$ of all free ultrafilters on $G$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-03-10T20:15:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "ramsey-product subset",
      "infinite group",
      "infinite subsets"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}