{
  "abstract": "For a group $G$, let $a(G)$ denote the minimum number of abelian subgroups covering $G$, and let $ω(G)$ be the maximum size of a pairwise noncommuting set. We prove the exact formula $\\sup_{ω(G)\\leq n}a(G)=2^{\\lfloor(n-1)/2\\rfloor}+1$ for every $n\\geq 63$. Equality holds precisely for groups with derived subgroup of order two and binary symplectic central quotient of dimension $2\\lfloor(n-1)/2\\rfloor$. The proof combines centralizer descent with a structural separation of nonscalar alternating commutator maps.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.22388",
  "author_total": 1,
  "authors": [
    {
      "name": "Guillaume Lecomte"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/882b2xp8eerkn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.22388",
  "fulltext_url": null,
  "id": "882b2xp8eerkn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.22388",
  "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.CO"
    ],
    [
      "arxiv",
      "math.GR"
    ],
    [
      "openalex",
      "2607|Finite Group Theory Research"
    ]
  ],
  "openalex": "W7222946457",
  "pdf_url": "https://arxiv.org/pdf/2610.22388",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/882b2xp8eerkn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:37Z",
      "native_id": "2610.22388",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.22388"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Eventual Exactness and Rigidity for Abelian Covers of Groups",
  "title_text": "Eventual Exactness and Rigidity for Abelian Covers of Groups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:31Z",
  "url": "https://research.draconitic.com/paper/882b2xp8eerkn",
  "venue": "arXiv",
  "versions": []
}