{
  "abstract": "Let G be the first Grigorchuk group. We show that the commutator width of G is 2 : every element g\\in [G,G] is a product of two commutators, and also of six conjugates of a . Furthermore, we show that every finitely generated subgroup H\\leq G has finite commutator width, which however can be arbitrarily large, and that G contains a subgroup of infinite commutator width. The proofs were assisted by the computer algebra system GAP.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 3,
  "authors": [
    {
      "name": "Laurent Bartholdi"
    },
    {
      "name": "Thorsten Groth"
    },
    {
      "name": "Igor Lysenok"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ekn4kyqy3vce1.bib",
  "cited_by": 7,
  "doi": "10.4171/ggd/666",
  "fulltext_url": null,
  "id": "ekn4kyqy3vce1",
  "issns": [
    "1661-7207",
    "1661-7215"
  ],
  "landing_url": "https://hal.science/hal-05849726v1",
  "language": "en",
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.math"
    ],
    [
      "hal",
      "1.math.math-gr"
    ],
    [
      "openalex",
      "2607|Finite Group Theory Research"
    ]
  ],
  "openalex": "W2765446779",
  "pdf_url": "https://ems.press/content/serial-article-files/25282",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-03",
  "publisher": "European Mathematical Society",
  "ris": "https://research.draconitic.com/paper/ekn4kyqy3vce1.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:20:19Z",
      "native_id": "hal-05849726",
      "source": "hal",
      "url": "https://hal.science/hal-05849726v1"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-gr",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Commutator width in the first Grigorchuk group",
  "title_text": "Commutator width in the first Grigorchuk group",
  "type": "peer-reviewed",
  "updated_at": "2026-11-05T12:20:12Z",
  "url": "https://research.draconitic.com/paper/ekn4kyqy3vce1",
  "venue": "Groups, Geometry, and Dynamics",
  "versions": []
}