{
  "id": "2008.02861",
  "version": "v1",
  "published": "2020-08-06T20:26:39.000Z",
  "updated": "2020-08-06T20:26:39.000Z",
  "title": "Commutator length of powers in free products of groups",
  "authors": [
    "Vadim Yu. Bereznyuk",
    "Anton A. Klyachko"
  ],
  "comment": "11 pages, 4 figures. A Russian version of this paper is at http://halgebra.math.msu.su/staff/klyachko/papers.htm",
  "categories": [
    "math.GR"
  ],
  "abstract": "Given groups $A$ and $B$, what is the minimal commutator length of the 2020th (for instance) power of an element $g\\in A*B$ not conjugate to elements of the free factors? The exhaustive answer to this question is still unknown, but we can give an almost answer: this minimum is one of two numbers (simply depending on $A$ and $B$). Other similar problems are also considered.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-08-06T20:26:39.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "free products",
      "minimal commutator length",
      "free factors",
      "similar problems",
      "exhaustive answer"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}