{
  "id": "1807.09086",
  "version": "v1",
  "published": "2018-07-24T13:19:14.000Z",
  "updated": "2018-07-24T13:19:14.000Z",
  "title": "The Möbius function of ${\\rm PSU}(3,2^{2^n})$",
  "authors": [
    "Giovanni Zini"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $G$ be the simple group ${\\rm PSU}(2,2^{2^n})$, $n>0$. For any subgroup $H$ of $G$, we compute the M\\\"obius function $\\mu_L(H,G)$ of $H$ in the subgroup lattice $L$ of $G$, and the M\\\"obius function $\\mu_{\\bar L}([H],[G])$ of $[H]$ in the poset $\\bar L$ of conjugacy classes of subgroups of $G$. For any prime $p$, we provide the Euler characteristic of the order complex of the poset of $p$-subgroups of $G$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-07-24T13:19:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20D30"
    ],
    "keywords": [
      "möbius function",
      "simple group",
      "subgroup lattice",
      "conjugacy classes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}