{
  "abstract": "We show that the Frobenius group $\\langle x,y,z\\mid x^p=y^p=z^4=1,\\ xy=yx,\\ zxz^{-1}=y,\\ zyz^{-1}=x^{-1}\\rangle$ of order $4p^2$ contains no $(4p^2,2p^2-p,p^2-p)$ difference set if $p\\equiv 3\\pmod 4$ is a prime with $p \\geq 7$. Together with results of McFarland, Iiams and Liebler this shows that no group of order $4p^2$ with $p \\equiv 3 \\pmod 4$ and $p \\geq 7$ contains a Hadamard difference set.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.37417",
  "author_total": 1,
  "authors": [
    {
      "name": "Bernhard Schmidt"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fnbav6cmjjy4h.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.37417",
  "fulltext_url": null,
  "id": "fnbav6cmjjy4h",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.37417",
  "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": "W7224101463",
  "pdf_url": "https://arxiv.org/pdf/2610.37417",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fnbav6cmjjy4h.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:53Z",
      "native_id": "2610.37417",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.37417"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Nonexistence of Hadamard difference sets in groups of order $4p^2$ with $p\\equiv 3 \\pmod 4$, $p\\ge 7$",
  "title_text": "Nonexistence of Hadamard difference sets in groups of order 4p^2 with p≡ 3 pmod 4, p≥ 7",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:53Z",
  "url": "https://research.draconitic.com/paper/fnbav6cmjjy4h",
  "venue": "arXiv",
  "versions": []
}