{
  "id": "1208.3177",
  "version": "v2",
  "published": "2012-08-15T18:59:07.000Z",
  "updated": "2012-08-16T00:42:02.000Z",
  "title": "Commutators of elements of coprime orders in finite groups",
  "authors": [
    "Pavel Shumyatsky"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "This paper is an attempt to find out which properties of a finite group G can be expressed in terms of commutators of elements of coprime orders. A criterion of solubility of G in terms of such commutators is obtained. We also conjecture that every element of a nonabelian simple group is a commutator of elements of coprime orders and we confirm this conjecture for the alternating groups.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-08-16T00:42:02.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "coprime orders",
      "finite group",
      "commutator",
      "nonabelian simple group",
      "conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1208.3177S"
    }
  }
}