{
  "abstract": "Let $H_{27}=\\mathrm{UT}_3(\\mathbb{F}_3)$ be the nonabelian group of order $27$ and exponent $3$. We prove that $\\mathsf{d}(H_{27}\\times C_3^r)=2r+6$ for every integer $r\\geq0$. The proof combines an affine coefficient identity in the group algebra of an elementary abelian group with a decomposition of the nonorthogonality graph of $\\mathbb{F}_3^2$ into eight edge-disjoint zero-sum triangles. It is uniform in $r$, does not use the value of the small Davenport constant for a smaller nonabelian group, and requires no computational enumeration.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.19810",
  "author_total": 1,
  "authors": [
    {
      "name": "Andreas Volkmann"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ae3t74t4yph86.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.19810",
  "fulltext_url": null,
  "id": "ae3t74t4yph86",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.19810",
  "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"
    ],
    [
      "arxiv",
      "math.GR"
    ],
    [
      "openalex",
      "2607|Finite Group Theory Research"
    ]
  ],
  "openalex": "W7213580017",
  "pdf_url": "https://arxiv.org/pdf/2609.19810",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ae3t74t4yph86.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:23Z",
      "native_id": "2609.19810",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.19810"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "The small Davenport constant of $H_{27}\\times C_3^r$",
  "title_text": "The small Davenport constant of H_27× C_3^r",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:23Z",
  "url": "https://research.draconitic.com/paper/ae3t74t4yph86",
  "venue": "arXiv",
  "versions": []
}