{
  "abstract": "The class-breadth conjecture of Leedham-Green, Neumann and Wiegold states that the nilpotency class of any $p$-group is at most $b(G) + 1$, where $\\displaystyle{b(G) = \\max_{g\\in G}\\log_p[G:Z_G(g)]}$ denotes the breadth of a group $G$. While several counter-examples to this conjecture have been found for $p = 2$, it is still open in general for $p > 2$. This article is dedicated to the general case $p > 2$ of the conjecture.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.13423",
  "author_total": 1,
  "authors": [
    {
      "name": "Alexander Skutin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8tmdmjd446dap.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.13423",
  "fulltext_url": null,
  "id": "8tmdmjd446dap",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.13423",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.GR"
    ],
    [
      "openalex",
      "2607|Finite Group Theory Research"
    ]
  ],
  "openalex": "W7164565289",
  "pdf_url": "https://arxiv.org/pdf/2606.13423",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8tmdmjd446dap.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2606.13423",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.13423"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "On the class-breadth conjecture for $p$-groups",
  "title_text": "On the class-breadth conjecture for p-groups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/8tmdmjd446dap",
  "venue": "arXiv",
  "versions": []
}