{
  "abstract": "Let F be a saturated fusion system on a finite 2-group S, and let B(F) be the Burnside ring of F. Barsotti and Carman proved that when S is abelian, B(F)^*=B(S)^* if and only if F=F_S(S). Barsotti and Carman asked on page 728 of their paper whether there exists a counterexample to Corollary 9.3 for a nonabelian 2-group. We have given a positive answer. Our main conclusion is that the following are equivalent for all finite 2-groups: (1)F=F_S(S); (2)B(F)^*=B(S)^*; (3)For every maximal subgroup M of S, 1-[S/M] is in B(F)^*.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.07970",
  "author_total": 2,
  "authors": [
    {
      "name": "Chunbo Zhou"
    },
    {
      "name": "Heguo Liu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7yt2xxmhhp5np.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.07970",
  "fulltext_url": null,
  "id": "7yt2xxmhhp5np",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.07970",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.07970",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7yt2xxmhhp5np.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T18:21:34Z",
      "native_id": "2611.07970",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.07970"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "A positive answer to Barsotti and Carman's question on unit groups of Burnside rings of fusion systems",
  "title_text": "A positive answer to Barsotti and Carman's question on unit groups of Burnside rings of fusion systems",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:48Z",
  "url": "https://research.draconitic.com/paper/7yt2xxmhhp5np",
  "venue": "arXiv",
  "versions": []
}