{
  "id": "math/0411463",
  "version": "v1",
  "published": "2004-11-21T18:43:25.000Z",
  "updated": "2004-11-21T18:43:25.000Z",
  "title": "Engel-like characterization of radicals in finite dimensional Lie algebras and finite groups",
  "authors": [
    "Tatiana Bandman",
    "Mikhail Borovoi",
    "Fritz Grunewald",
    "Boris Kunyavskii",
    "Eugene Plotkin"
  ],
  "comment": "17 pages",
  "journal": "Manuscripta Math. 119 (2006), 365-381",
  "categories": [
    "math.GR",
    "math.RA"
  ],
  "abstract": "A classical theorem of R. Baer describes the nilpotent radical of a finite group G as the set of all Engel elements, i.e. elements y in G such that for any x in G the n-th commutator [x,y,...,y] equals 1 for n big enough. We obtain a characterization of the solvable radical of a finite dimensional Lie algebra defined over a field of characteristic zero in similar terms. We suggest a conjectural description of the solvable radical of a finite group as the set of Engel-like elements and reduce this conjecture to the case of a finite simple group.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-11-21T18:43:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20D25",
      "17B05",
      "17B01"
    ],
    "keywords": [
      "finite group",
      "engel-like characterization",
      "finite simple group",
      "finite dimensional lie algebra",
      "characteristic zero"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math.....11463B"
    }
  }
}