{
  "id": "1112.4559",
  "version": "v1",
  "published": "2011-12-20T03:50:32.000Z",
  "updated": "2011-12-20T03:50:32.000Z",
  "title": "Lifting in Frattini Covers and A Characterization of Finite Solvable Groups",
  "authors": [
    "Robert Guralnick",
    "Pham Huu Tiep"
  ],
  "categories": [
    "math.GR",
    "math.AG",
    "math.RT"
  ],
  "abstract": "We prove a lifting theorem for odd Frattini covers of finite groups. Using this, we characterize solvable groups and more generally p-solvable groups in terms of containing a triple of elements of distinct prime power orders with product 1. This is also related to various questions about Fried's modular tower program and properties of Hurwitz spaces of covers of curves.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-12-20T03:50:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20D10",
      "20D06",
      "20D05",
      "14G32",
      "14H30"
    ],
    "keywords": [
      "finite solvable groups",
      "characterization",
      "frieds modular tower program",
      "distinct prime power orders",
      "odd frattini covers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1112.4559G"
    }
  }
}