{
  "abstract": "For an element $g$ of a group $G$, a right Engel sink of $g$ is a subset of $G$ containing all sufficiently long commutators $[...[[g ,x],x],\\dots ,x]$ for all $x\\in G$. A left Engel sink of $g$ is a subset of $G$ containing all sufficiently long commutators $[...[[x ,g ],g ],\\dots ,g]$ for all $x\\in G$. Using the classification of finite simple groups we prove that if a finite group $G$ has an element $g$ such that $G=[G,g]$, then the order of $G$ is bounded in terms of a right Engel sink of $g$, as well as in terms of a left Engel sink of $g$. Earlier Guralnick and Tracey proved this in the case where $g$ is an involution without using the classification.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.08607",
  "author_total": 2,
  "authors": [
    {
      "name": "Evgeny Khukhro"
    },
    {
      "name": "Pavel Shumyatsky"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b4fc4mmm59dgm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.08607",
  "fulltext_url": null,
  "id": "b4fc4mmm59dgm",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.08607",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.GR"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2605.08607",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-31",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b4fc4mmm59dgm.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:48Z",
      "native_id": "2605.08607",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.08607"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "On finite groups containing an element whose Engel sink is small",
  "title_text": "On finite groups containing an element whose Engel sink is small",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/b4fc4mmm59dgm",
  "venue": "arXiv",
  "versions": []
}