{
  "id": "2103.12148",
  "version": "v1",
  "published": "2021-03-22T19:46:05.000Z",
  "updated": "2021-03-22T19:46:05.000Z",
  "title": "A New Maximal Subgroup of $E_8$ in Characteristic $3$",
  "authors": [
    "David A. Craven",
    "David I. Stewart",
    "Adam R. Thomas"
  ],
  "comment": "9 pages",
  "categories": [
    "math.GR"
  ],
  "abstract": "We prove the existence and uniqueness of a new maximal subgroup of the algebraic group of type $E_8$ in characteristic $3$. This has type $F_4$, and was missing from previous lists of maximal subgroups produced by Seitz and Liebeck--Seitz. We also prove a result about the finite group $H={}^3\\!D_4(2)$, that if $H$ embeds in $E_8$ (in any characteristic $p$) and has two composition factors on the adjoint module then $p=3$ and $H$ lies in this new maximal $F_4$ subgroup.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-03-22T19:46:05.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "maximal subgroup",
      "characteristic",
      "algebraic group",
      "finite group",
      "composition factors"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}