{
  "abstract": "Let $G$ be a finite group. We prove that the order of the abelianization $G/G'$ divides the order of $H^{2m}(G,\\mathbb{Z})$ for every $m\\geq1$. As a consequence, for a field $K$, nonvanishing of $Ext^1_{KG}(K,K)$ implies nonvanishing of $Ext^n_{KG}(K,K)$ for every $n\\geq1$. This answers a conjecture by Erdmann, Klász and Marczinzik. We use this to show that the Hochschild cohomology of $KG$ is nonzero in every nonnegative degree whenever the characteristic of $K$ divides $|G|$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.24573",
  "author_total": 2,
  "authors": [
    {
      "name": "Tiago Cruz"
    },
    {
      "name": "Rene Marczinzik"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3zjrbgbrx1kac.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.24573",
  "fulltext_url": null,
  "id": "3zjrbgbrx1kac",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.24573",
  "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.GR"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2602|Advanced Topics in Algebra"
    ]
  ],
  "openalex": "W7214044721",
  "pdf_url": "https://arxiv.org/pdf/2609.24573",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3zjrbgbrx1kac.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.24573",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.24573"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Nonvanishing of cohomology for groups",
  "title_text": "Nonvanishing of cohomology for groups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/3zjrbgbrx1kac",
  "venue": "arXiv",
  "versions": []
}