{
  "id": "1408.6259",
  "version": "v1",
  "published": "2014-08-26T21:06:42.000Z",
  "updated": "2014-08-26T21:06:42.000Z",
  "title": "A conjecture on partitions of groups",
  "authors": [
    "Igor Protasov",
    "Sergii Slobodianiuk"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "We conjecture that every infinite group $G$ can be partitioned into countably many cells $G=\\bigcup_{n\\in\\omega}A_n$ such that $cov(A_nA_n^{-1})=|G|$ for each $n\\in\\omega$. Here $cov(A)=\\min\\{|X|:X\\subseteq G, G=XA\\}$. We confirm this conjecture for each group of regular cardinality and for some groups (in particular, Abelian) of an arbitrary cardinality.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-08-26T21:06:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E05",
      "20B07",
      "20F69"
    ],
    "keywords": [
      "conjecture",
      "partitions",
      "infinite group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1408.6259P"
    }
  }
}