{
  "id": "1510.00586",
  "version": "v1",
  "published": "2015-10-02T13:20:25.000Z",
  "updated": "2015-10-02T13:20:25.000Z",
  "title": "The small index property of automorphism groups of ab-initio generic structures",
  "authors": [
    "Zaniar Ghadernezhad"
  ],
  "comment": "15 pages",
  "categories": [
    "math.LO",
    "math.GR"
  ],
  "abstract": "Suppose $M$ is a countable ab-initio (uncollapsed) generic structure which is obtained from a pre-dimension function with rational coefficients. We show that if $H$ is a subgroup of $\\mbox{Aut}\\left(M\\right)$ with $\\left[\\mbox{Aut}\\left(M\\right):H\\right]<2^{\\aleph_{0}}$, then there exists a finite set $A\\subseteq M$ such that $\\mbox{Aut}_{A}\\left(M\\right)\\subseteq H$. This shows that $\\mbox{Aut}\\left(M\\right)$ has the small index property.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-10-02T13:20:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03C15",
      "20B07",
      "20B27"
    ],
    "keywords": [
      "small index property",
      "ab-initio generic structures",
      "automorphism groups",
      "pre-dimension function",
      "rational coefficients"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}