{
  "abstract": "We show that a discrete group is hermitian if and only if it is FC-hypercentral, that is, if and only if it does not have any nontrivial ICC quotients. In particular, a finitely generated group is hermitian if and only if it is virtually nilpotent. The main step is an elementary, self-contained proof that every hermitian ICC group is trivial, based on a finite-set separation property of nontrivial ICC groups.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.40226",
  "author_total": 1,
  "authors": [
    {
      "name": "Tron Omland"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6d2czmm1mjdat.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.40226",
  "fulltext_url": null,
  "id": "6d2czmm1mjdat",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.40226",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.FA"
    ],
    [
      "arxiv",
      "math.GR"
    ],
    [
      "arxiv",
      "math.OA"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.40226",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6d2czmm1mjdat.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.40226",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.40226"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Discrete hermitian groups are FC-hypercentral",
  "title_text": "Discrete hermitian groups are FC-hypercentral",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/6d2czmm1mjdat",
  "venue": "arXiv",
  "versions": []
}