{
  "abstract": "For $k\\geq 1$ , we say that a finite group $G$ satisfies property $\\mathcal P_k$ if, for every $β_1,\\ldots,β_k\\in\\operatorname{Aut}(G)$, there exists a bijection $f$ of $G$ such that each map $g\\mapsto β_i(g)f(g)$ is a bijection. For $k=1$ this is equivalent to the classical Hall--Paige complete mapping property. We prove that if $p$ is the smallest prime divisor of $|G|$, then $G$ satisfies $\\mathcal P_k$ for every $k<p-1$ and we show that this bound is sharp. For finite abelian $p$-groups, the bijection $f$ may moreover be chosen to be an automorphism, and for noncyclic homocyclic $p$-groups this remains true for $k=p-1$. Finally, we interpret $\\mathcal P_k$ in terms of common transversals and common orthogonal mates of Latin squares generated from automorphisms and the Cayley table of a finite group $G$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.21600",
  "author_total": 1,
  "authors": [
    {
      "name": "Maria Loukaki"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1ggw26n1k12rf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.21600",
  "fulltext_url": null,
  "id": "1ggw26n1k12rf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.21600",
  "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": "W7222504279",
  "pdf_url": "https://arxiv.org/pdf/2610.21600",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1ggw26n1k12rf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:38Z",
      "native_id": "2610.21600",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.21600"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "A simultaneous variant of the Hall-Paige theorem and applications",
  "title_text": "A simultaneous variant of the Hall-Paige theorem and applications",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/1ggw26n1k12rf",
  "venue": "arXiv",
  "versions": []
}