{
  "id": "1212.3520",
  "version": "v2",
  "published": "2012-12-14T16:36:10.000Z",
  "updated": "2014-08-17T01:50:40.000Z",
  "title": "Ramsey theory for p-quasicyclic groups with a view towards topological dynamics",
  "authors": [
    "Andreas Koutsogiannis"
  ],
  "comment": "26 pages. arXiv admin note: substantial text overlap with arXiv:1101.3226 This paper has been withdrawn by the author for further research",
  "categories": [
    "math.CO",
    "math.GN"
  ],
  "abstract": "We prove additive and multiplicative partition theorems, obtaining combinatorial results for p-quasicyclic groups, where p is a prime number. We also get density results for p-quasicyclic groups via left F{\\o}lner sequences of non-empty finite subsets of it, giving a sufficient condition in order a subset of a p-quasicyclic group to contain arbitrary long arithmetic progressions. Finally, we introduce the notion of a dynamical system over p-quasicyclic groups extending the classical notion of a topological dynamical system and we prove (multiple) recurrent results for the p-quasicyclic groups. In particular, we prove recurrent results analogous to Furstenberg-Weiss type theorems for classical systems.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-08-17T01:50:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "p-quasicyclic group",
      "ramsey theory",
      "topological dynamics",
      "contain arbitrary long arithmetic progressions",
      "recurrent results"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1212.3520K"
    }
  }
}