{
  "id": "1411.0180",
  "version": "v1",
  "published": "2014-11-01T23:10:15.000Z",
  "updated": "2014-11-01T23:10:15.000Z",
  "title": "The automorphism group of a shift of linear growth: beyond transitivity",
  "authors": [
    "Van Cyr",
    "Bryna Kra"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "For a finite alphabet $\\mathcal{A}$ and shift $X\\subseteq\\mathcal{A}^{\\mathbb{Z}}$ whose factor complexity function grows at most linearly, we study the algebraic properties of the automorphism group ${\\rm Aut}(X)$. For such systems, we show that every finitely generated subgroup of ${\\rm Aut}(X)$ is virtually ${\\mathbb Z}^d$, in contrast to the behavior when the complexity function grows more quickly. With additional dynamical assumptions we show more: if $X$ is transitive, then ${\\rm Aut}(X)$ is virtually $\\mathbb Z$; if $X$ has dense aperiodic points, then ${\\rm Aut}(X)$ is virtually ${\\mathbb Z}^d$. We also classify all finite groups that arise as the automorphism group of a shift.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-11-01T23:10:15.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "automorphism group",
      "linear growth",
      "factor complexity function grows",
      "transitivity",
      "dense aperiodic points"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1411.0180C"
    }
  }
}