{
  "id": "1603.05909",
  "version": "v1",
  "published": "2016-03-18T16:28:17.000Z",
  "updated": "2016-03-18T16:28:17.000Z",
  "title": "Acylindrical hyperbolicity, non simplicity and SQ-universality of groups splitting over Z",
  "authors": [
    "J. O. Button"
  ],
  "comment": "Much shorter version of 1509.05688 with strengthening of main result",
  "categories": [
    "math.GR"
  ],
  "abstract": "We show, using acylindrical hyperbolicity, that a finitely generated group splitting over $\\Z$ cannot be simple. We also obtain SQ-universality in most cases, for instance a balanced group (one where if two powers of an infinite order element are conjugate then they are equal or inverse) which is finitely generated and splits over $\\Z$ must either be SQ-universal or it is one of exactly seven virtually abelian exceptions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-03-18T16:28:17.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "acylindrical hyperbolicity",
      "non simplicity",
      "groups splitting",
      "sq-universality",
      "infinite order element"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160305909B"
    }
  }
}