{
  "id": "1608.02492",
  "version": "v1",
  "published": "2016-08-04T05:34:58.000Z",
  "updated": "2016-08-04T05:34:58.000Z",
  "title": "Regular subgroups of the affine group with no translations",
  "authors": [
    "M. A. Pellegrini",
    "M. C. Tamburini Bellani"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "Given a regular subgroup R of AGL_n(F), one can ask if R contains nontrivial translations. A negative answer to this question was given by Liebeck, Praeger and Saxl for AGL_2(p) (p prime), AGL_3(p) (p odd) and for AGL_4(2). A positive answer was given by Hegedus for AGL_n(p) when n >= 4 if p is odd and for n=3 or n >=5 if p=2. A first generalization to finite fields of Hegedus' construction was recently obtained by Catino, Colazzo and Stefanelli. In this paper we construct examples of such subgroups in AGL_n(F) for any n >= 5 and any field F. For n < 5 we provide necessary and sufficient conditions for their existence, assuming F to be finite in certain cases.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-08-04T05:34:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20B35",
      "15A63",
      "15A21"
    ],
    "keywords": [
      "regular subgroup",
      "affine group",
      "contains nontrivial translations",
      "sufficient conditions",
      "first generalization"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}