{
  "abstract": "We give an algebraic criterion for certain sequences $(G_n)_{n\\in\\mathbb{N}}$ of groups to have Kazhdan's property $(T)$ eventually. As a consequence, we prove that the Brin--Thompson groups $nV$ have Kazhdan's property $(T)$ for large $n$. The algebraic criterion provides a uniform proof that $nV$, $\\mathrm{Aut}(F_n)$ and $\\mathrm{EL}_n(R)$ for a finitely generated associative unital ring $R$ have property $(T)$ for large $n$. In an appendix, written by Francesco Fournier-Facio, it is shown that the group $nV$ for large $n$ is neither hyperlinear, in particular not sofic, nor $\\mathrm{MF}$. Further, it is not Schatten $p$-approximable for any $1\\le p<\\infty$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.09524",
  "author_total": 3,
  "authors": [
    {
      "name": "Francesco Fournier-Facio"
    },
    {
      "name": "Roman Sauer"
    },
    {
      "name": "Eduard Schesler"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/34gg5rkvp50tg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.09524",
  "fulltext_url": null,
  "id": "34gg5rkvp50tg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.09524",
  "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"
    ],
    [
      "openalex",
      "2610|Advanced Operator Algebra Research"
    ]
  ],
  "openalex": "W7220950491",
  "pdf_url": "https://arxiv.org/pdf/2610.09524",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/34gg5rkvp50tg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.09524",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.09524"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Higher Brin--Thompson groups are Kazhdan",
  "title_text": "Higher Brin--Thompson groups are Kazhdan",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/34gg5rkvp50tg",
  "venue": "arXiv",
  "versions": []
}