{
  "abstract": "For a finite group $G$ and a subset $S\\subseteq G$, the bi-Cayley graph $\\operatorname{BCay}(G,S)$ has vertex set $G\\times\\{0,1\\}$ and edges $\\{(x,0),(sx,1)\\}$ for $x\\in G$ and $s\\in S$. The group $G$ is called an $m$-BCI-group if, for all subsets $S,T\\subseteq G$ with $|S|\\leq m$, the isomorphism $\\operatorname{BCay}(G,S)\\cong\\operatorname{BCay}(G,T)$ implies that $T=gS^α$ for some $g\\in G$ and $α\\in\\operatorname{Aut} G$. We prove that, for every prime $p$, the generalized quaternion group $Q_{4p}$ is a $4$-BCI-group. For $p\\geq5$, the proof uses regular coverings and voltage assignments: we pass to quotient graphs modulo the Sylow $p$-subgroup and lift isomorphisms between them.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.25378",
  "author_total": 1,
  "authors": [
    {
      "name": "Jin-Hua Xie"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/747y3d7f3ezhx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.25378",
  "fulltext_url": null,
  "id": "747y3d7f3ezhx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.25378",
  "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.CO"
    ],
    [
      "openalex",
      "2607|Finite Group Theory Research"
    ]
  ],
  "openalex": "W7223005836",
  "pdf_url": "https://arxiv.org/pdf/2610.25378",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/747y3d7f3ezhx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.25378",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.25378"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Generalized quaternion groups of order $4p$ are $4$-BCI-groups",
  "title_text": "Generalized quaternion groups of order 4p are $4$-BCI-groups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/747y3d7f3ezhx",
  "venue": "arXiv",
  "versions": []
}