{
  "abstract": "We show that for every finite group $G$ and every integer $n$, the Nil group $\\mathrm{NK}_n(\\mathbb{Z}[G])$ of the integral group ring of $G$ has finite exponent, and give a bound depending on n and the order $|G|$. This bound is explicit when every prime divisor of $|G|$ is at least $3+n/2$. More generally, our finite exponent result applies to $\\mathrm{NK}_n(R[G])$ whenever $R$ is a regular, torsion-free, Noetherian commutative ring such that $R/p$ is regular for every prime $p$ that divides $|G|$. In the Appendix, M. Morrow provides an alternative approach and also shows that the Nil group $\\mathrm{NK}_n(X)$ of an excellent Noetherian scheme $X$, with $X[1/p]$ regular, is annihilated by a finite power of $p$, provided $X$ admits a suitable resolution of singularities. By extending his argument to certain noncommutative rings, we also show that, for $R$ as above and $α$ any automorphism of $G$, the Farrell Nil groups $\\mathrm{NK}_n(R[G],α)$ have finite exponent. As a consequence, for every virtually cyclic group $Γ$, the group $\\mathrm{K}_n(\\mathbb{Z}[Γ])$ is a direct sum of a finitely generated abelian group and an infinite countable direct sum of copies of a finite abelian group.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.13908",
  "author_total": 4,
  "authors": [
    {
      "name": "Ted Chinburg"
    },
    {
      "name": "Matthew Morrow"
    },
    {
      "name": "Georgios Pappas"
    },
    {
      "name": "Martin J. Taylor"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/drew25t5rqvk7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.13908",
  "fulltext_url": null,
  "id": "drew25t5rqvk7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.13908",
  "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.AT"
    ],
    [
      "arxiv",
      "math.KT"
    ],
    [
      "openalex",
      "2610|Homotopy and Cohomology in Algebraic Topology"
    ]
  ],
  "openalex": "W7213227620",
  "pdf_url": "https://arxiv.org/pdf/2609.13908",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/drew25t5rqvk7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.13908",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.13908"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.KT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "The Nil K-groups of finite groups",
  "title_text": "The Nil K-groups of finite groups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/drew25t5rqvk7",
  "venue": "arXiv",
  "versions": []
}