{
  "id": "1706.00626",
  "version": "v1",
  "published": "2017-06-02T11:01:18.000Z",
  "updated": "2017-06-02T11:01:18.000Z",
  "title": "A geometric simulation theorem on direct products of finitely generated groups",
  "authors": [
    "Sebastián Barbieri"
  ],
  "comment": "23 pages, 3 very beautiful figures",
  "categories": [
    "math.DS"
  ],
  "abstract": "We show that every effectively closed action of a finitely generated group $G$ over a Cantor set can be obtained as a topological factor of the $G$-subaction of a $(G \\times H_1 \\times H_2)$-subshift of finite type for any choice of infinite and finitely generated groups $H_1,H_2$. As a consequence, we obtain that every group of the form $G_1 \\times G_2 \\times G_3$ admits a non-empty strongly aperiodic SFT subject to the condition that each $G_i$ is finitely generated and has decidable word problem. As a corollary of this last result we prove the existence of a non-empty strongly aperiodic SFT in the Grigorchuk group.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-06-02T11:01:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37B10",
      "37B50"
    ],
    "keywords": [
      "finitely generated group",
      "geometric simulation theorem",
      "direct products",
      "non-empty strongly aperiodic sft subject",
      "finite type"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}