{
  "abstract": "Given a finite group $G$, its order sequence $os(G)$ is a sequence formed of the element orders of $G$ written in non-decreasing order. In [Electron. J. Combin. 32 (2025), no. 2, Paper No. 2.9], P. J. Cameron and H. K. Dey proved that if $G$ and $H$ are groups of coprime orders, $G$ is abelian and $K$ is any extension of $G$ by $H$, then there is a bijection $f$ from $G\\times H$ to $K$ such that the order of $f(x)$ divides the order of $x$, for all $x\\in G\\times H$. In the same paper, the authors asked if the hypothesis ``$G$ is abelian\" is necessary. We show that if this condition is dropped, the result does not hold in general.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.24950",
  "author_total": 1,
  "authors": [
    {
      "name": "Mihai-Silviu Lazorec"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1rx3r9gsafymt.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.24950",
  "fulltext_url": null,
  "id": "1rx3r9gsafymt",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.24950",
  "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": "W7223050141",
  "pdf_url": "https://arxiv.org/pdf/2610.24950",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1rx3r9gsafymt.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.24950",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.24950"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "On the strong domination relation of order sequences for some group extensions",
  "title_text": "On the strong domination relation of order sequences for some group extensions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/1rx3r9gsafymt",
  "venue": "arXiv",
  "versions": []
}