{
  "id": "1708.07831",
  "version": "v1",
  "published": "2017-08-25T17:31:37.000Z",
  "updated": "2017-08-25T17:31:37.000Z",
  "title": "On the automorphism group of the m-coloured random graph",
  "authors": [
    "Peter J. Cameron",
    "Sam Tarzi"
  ],
  "comment": "Paper from 2007 placed here because of renewed interest in the topic. arXiv admin note: substantial text overlap with arXiv:1406.7870",
  "categories": [
    "math.CO",
    "math.GR"
  ],
  "abstract": "Let $R_m$ be the (unique) universal homogeneous $m$-edge-coloured countable complete graph ($m\\ge2$), and $G_m$ its group of colour-preserving automorphisms. The group $G_m$ was shown to be simple by John Truss. We examine the automorphism group of $G_m$, and show that it is the group of permutations of $R_m$ which induce permutations on the colours, and hence an extension of $G_m$ by the symmetric group of degree $m$. We show further that the extension splits if and only if $m$ is odd, and in the case where $m$ is even and not divisible by~$8$ we find the smallest supplement for $G_m$ in its automorphism group. (This unpublished paper from 2007 is placed here because of renewed interest in the topic.)",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-08-25T17:31:37.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "automorphism group",
      "m-coloured random graph",
      "smallest supplement",
      "john truss",
      "edge-coloured countable complete graph"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}