{
  "id": "1112.2721",
  "version": "v2",
  "published": "2011-12-12T21:16:23.000Z",
  "updated": "2016-01-13T16:58:31.000Z",
  "title": "The geometry of the conjugacy problem in lamplighter groups",
  "authors": [
    "Andrew W. Sale"
  ],
  "comment": "13 pages, 6 figure. Updated to focus only on lamplighter groups and their generalisations. The other aspects of v1 have appeared in other papers of the author",
  "categories": [
    "math.GR",
    "math.MG"
  ],
  "abstract": "In this note we investigate the conjugacy problem in lamplighter groups with particular interest in the role of their geometry. In particular we show that the conjugacy length function is linear.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-12-12T21:16:23.000Z",
      "title": "Short Conjugators in Solvable Groups",
      "abstract": "We give an upper bound on the size of short conjugators in certain solvable groups. Diestel-Leader graphs, which are a horocyclic product of trees, are discussed briefly and used to study the lamplighter groups. The other solvable groups we look at can be recognised in a similar vein, as groups which act on a horocyclic product of well known spaces. These include the Baumslag-Solitar groups BS(1,q) and semidirect products of Z^n with Z^k. Results can also be applied to the conjugacy of parabolic elements in Hilbert modular groups and to elements in 3-manifold groups.",
      "comment": "19 pages, 4 figures",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2016-01-13T16:58:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F65",
      "20F16",
      "20F10",
      "05C50",
      "20E22"
    ],
    "keywords": [
      "conjugacy problem",
      "lamplighter groups",
      "conjugacy length function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1112.2721S"
    }
  }
}