{
  "id": "1801.10065",
  "version": "v1",
  "published": "2018-01-30T15:53:03.000Z",
  "updated": "2018-01-30T15:53:03.000Z",
  "title": "Topological generation of linear algebraic groups I",
  "authors": [
    "Spencer Gerhardt"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "Let $C_1,...,C_e$ be noncentral conjugacy classes of the algebraic group $G=SL_n(k)$ defined over a sufficiently large field $k$, and let $\\Omega:=C_1\\times ...\\times C_e$. This paper determines necessary and sufficient conditions for the existence of a tuple $(x_1,...,x_e)\\in\\Omega$ such that $\\langle x_1,...,x_e\\rangle$ is Zariski dense in $G$. As a consequence, a new result concerning generic stabilizers in linear representations of algebraic groups is proved, and existing results on random $(r,s)$-generation of finite groups of Lie type are strengthened.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-01-30T15:53:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20G15"
    ],
    "keywords": [
      "linear algebraic groups",
      "topological generation",
      "result concerning generic stabilizers",
      "paper determines necessary",
      "noncentral conjugacy classes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}