{
  "abstract": "In 2010. Okuyama proved the following. Let $G$ be a finite group and $k$ an algebraically closed field of characteristic $p$ dividing the order of $G$. (1) Let $\\frak p$ be an associated prime of $H^*(G,k)$ of $\\dim=s$. Then there exists an elementary abelian $p$-subgroup $E\\subseteq G$ of rank $s$ with $\\mathfrak p=\\mathfrak p_E$ and depth$\\,H^*(C_GE,k)=s$. (2) Let $E$ be an elementary abelian $p$-subgroup of $G$ of rank $s$ and suppose depth$\\,H^*(C_GE,k)=s$. Then $\\mathfrak p_E$ is an associated prime of $H^*(G,k)$. It is shown this result is true for all fields of characteristic $p$. We also show the following result: If $E$ is an elementary abelian $p$-subgroup of $G$ and depth $H^*(G,k)=\\text{rank} E$, then up to conjugation $E$ contains the maximal elementary abelian subgroup contained in the center of a Sylow $p$-subgroup of $G$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.03569",
  "author_total": 1,
  "authors": [
    {
      "name": "James A. Schafer"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3g5eb8b3xq1h9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.03569",
  "fulltext_url": null,
  "id": "3g5eb8b3xq1h9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.03569",
  "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.AC"
    ],
    [
      "arxiv",
      "math.GR"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.03569",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3g5eb8b3xq1h9.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:14Z",
      "native_id": "2611.03569",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.03569"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Associated primes in group cohomology and a strange result",
  "title_text": "Associated primes in group cohomology and a strange result",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:28Z",
  "url": "https://research.draconitic.com/paper/3g5eb8b3xq1h9",
  "venue": "arXiv",
  "versions": []
}