{
  "abstract": "We study the Gorenstein homological dimension $Ghd_k G$ of groups $G$ which are of type $FP_{\\infty}$ over a commutative ring $k$. Our main result shows that, over an arbitrary ring $R$, every finitely presented Gorenstein flat $R$-module is projectively coresolved Gorenstein flat. Consequently, for a group $G$ of type $FP_\\infty$ over $k$ with sfli$k<\\infty$, the three natural dimensions for $G$, namely Gorenstein homological, Gorenstein cohomological and projectively coresolved Gorenstein flat, all coincide. Building on this collapse, we establish a Gorenstein homological analogue of Fel$'$dman's theorem, a formula for iterated $m$-fold self-extensions of a group $N$ of type $FP_\\infty$ over $\\mathbb Z$, and a field-detection theorem, showing that the Gorenstein homological dimension of a group of type $FP_\\infty$ over a principal ideal domain is realized after passing to a suitable field.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.08747",
  "author_total": 1,
  "authors": [
    {
      "name": "Dimitra-Dionysia Stergiopoulou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/00x8sew2yv5e5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.08747",
  "fulltext_url": null,
  "id": "00x8sew2yv5e5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.08747",
  "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.RA"
    ],
    [
      "openalex",
      "2602|Rings, Modules, and Algebras"
    ]
  ],
  "openalex": "W7202178463",
  "pdf_url": "https://arxiv.org/pdf/2608.08747",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/00x8sew2yv5e5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2608.08747",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.08747"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Gorenstein homological dimension of group extensions",
  "title_text": "Gorenstein homological dimension of group extensions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/00x8sew2yv5e5",
  "venue": "arXiv",
  "versions": []
}