{
  "id": "1706.06937",
  "version": "v1",
  "published": "2017-06-21T14:43:14.000Z",
  "updated": "2017-06-21T14:43:14.000Z",
  "title": "Weak commutativity and finiteness properties of groups",
  "authors": [
    "Martin R Bridson",
    "Dessislava H Kochloukova"
  ],
  "comment": "12 pages, 2 figures",
  "categories": [
    "math.GR"
  ],
  "abstract": "We consider the group $\\mathfrak{X}(G)$ obtained from $G\\ast G$ by forcing each element $g$ in the first free factor to commute with the copy of $g$ in the second free factor. Deceptively complicated finitely presented groups arise from this construction: $\\mathfrak{X}(G)$ is finitely presented if and only if $G$ is finitely presented, but if $F$ is a non-abelian free group of finite rank then $\\mathfrak{X}(F)$ has a subgroup of finite index whose third homology is not finitely generated.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-06-21T14:43:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F05",
      "20J05",
      "20E06"
    ],
    "keywords": [
      "finiteness properties",
      "weak commutativity",
      "non-abelian free group",
      "second free factor",
      "first free factor"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}