{
  "id": "1806.02753",
  "version": "v1",
  "published": "2018-06-07T16:14:13.000Z",
  "updated": "2018-06-07T16:14:13.000Z",
  "title": "A remark on Liouville property of strongly transitive actions",
  "authors": [
    "Kate Juschenko"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "Liouville property of actions of discrete groups can be reformulated in terms of existence co-F$\\o$lner sets. Since every action of amenable group is Liouville, the property can be served as an approach for proving non-amenability. The verification of this property is conceptually different than finding a non-amenable action. There are many groups that are defined by strongly transitive actions. In some cases amenability of such groups is an open problem. We define $n$-Liouville property of action to be Liouville property of point-wise action of the group on the sets of cardinality $n$. We reformulate $n$-Liouville property in terms of additive combinatorics and prove it for $n=1, 2$. The case $n\\geq 3$ remains open.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-06-07T16:14:13.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "liouville property",
      "strongly transitive actions",
      "remains open",
      "existence co-f",
      "open problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}