{
  "id": "2012.10116",
  "version": "v1",
  "published": "2020-12-18T09:17:36.000Z",
  "updated": "2020-12-18T09:17:36.000Z",
  "title": "Automorphisms of (Affine) SL(2,q)-Unitals",
  "authors": [
    "Verena Möhler"
  ],
  "comment": "15 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "$\\operatorname{SL}(2,q)$-unitals are unitals of order $q$ admitting a regular action of $\\operatorname{SL}(2,q)$ on the complement of some block. They can be obtained from affine $\\operatorname{SL}(2,q)$-unitals via parallelisms. We compute a sharp upper bound for automorphism groups of affine $\\operatorname{SL}(2,q)$-unitals and show that exactly two parallelisms are fixed by all automorphisms. In $\\operatorname{SL}(2,q)$-unitals obtained as closures of affine $\\operatorname{SL}(2,q)$-unitals via those two parallelisms, we show that there is one block fixed under the full automorphism group.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-12-18T09:17:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "51A10",
      "05E18"
    ],
    "keywords": [
      "full automorphism group",
      "parallelisms",
      "sharp upper bound",
      "regular action",
      "complement"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}