{
  "id": "1206.6340",
  "version": "v1",
  "published": "2012-06-27T17:14:50.000Z",
  "updated": "2012-06-27T17:14:50.000Z",
  "title": "On extendability of permutations",
  "authors": [
    "Mark Pankov"
  ],
  "categories": [
    "math.GR",
    "math.CO",
    "math.RT"
  ],
  "abstract": "Let $V$ be a left vector space over a division ring and let ${\\mathcal P}(V)$ be the associated projective space. We describe all finite subsets $X\\subset V$ such that every permutation on $X$ can be extended to a linear automorphism of $V$ and all finite subsets ${\\mathcal X}\\subset {\\mathcal P}(V)$ such that every permutation on ${\\mathcal X}$ can be extended to an element of ${\\rm PGL}(V)$. Also, we reformulate the results in terms of linear and projective representations of symmetric groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-06-27T17:14:50.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "permutation",
      "extendability",
      "finite subsets",
      "left vector space",
      "symmetric groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1206.6340P"
    }
  }
}