{
  "id": "1801.09863",
  "version": "v1",
  "published": "2018-01-30T06:53:45.000Z",
  "updated": "2018-01-30T06:53:45.000Z",
  "title": "Burnside groups and $n$-moves for links",
  "authors": [
    "Haruko A. Miyazawa",
    "Kodai Wada",
    "Akira Yasuhara"
  ],
  "comment": "6 pages, 5 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "Let $n$ be a positive integer. M. K. Dabkowski and J. H. Przytycki introduced the $n$th Burnside group of links which is preserved by $n$-moves, and proved that for any odd prime $p$ there exist links which are not equivalent to trivial links up to $p$-moves by using their $p$th Burnside groups. This gives counterexamples for the Montesinos-Nakanishi $3$-move conjecture. In general, it is hard to distinguish $p$th Burnside groups of a given link and a trivial link. We give a necessary condition for which $p$th Burnside groups are isomorphic to those of trivial links. The necessary condition gives us an efficient way to distinguish $p$th Burnside groups of a given link and a trivial link. As an application, we show that there exist links, each of which is not equivalent to a trivial link up to $p$-moves for any odd prime $p$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-01-30T06:53:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "57M27",
      "20F50"
    ],
    "keywords": [
      "th burnside group",
      "trivial link",
      "odd prime",
      "necessary condition",
      "move conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}