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Eventual Exactness and Rigidity for Abelian Covers of Groups — arXiv:2610.22388

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.22388
License (as archived): CC0-1.0
Archived: 2026-10-19T09:39:28.935Z
SHA-256 of the archived text: a8262cb051d0c2ce7a2dd057d546206a50b7b94a08b360c569aecc43f384ac45
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Eventual Exactness and Rigidity for Abelian Covers of Groups — arXiv:2610.22388 — arXiv (en), https://arxiv.org/abs/2610.22388 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_f16ef44edabc (Metraipolis archive dc_f16ef44edabc, sha256 a8262cb051d0c2ce7a2dd057d546206a50b7b94a08b360c569aecc43f384ac45)

BibTeX

@misc{dcf16ef44edabc,
  title = {Eventual Exactness and Rigidity for Abelian Covers of Groups — arXiv:2610.22388},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.22388},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_f16ef44edabc; sha256 a8262cb051d0c2ce7a2dd057d546206a50b7b94a08b360c569aecc43f384ac45},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.22388. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

For a group $G$, let $a(G)$ denote the minimum number of abelian subgroups covering $G$, and let $\omega(G)$ be the maximum size of a pairwise noncommuting set. We prove the exact formula $\sup_{\omega(G)\leq n}a(G)=2^{\lfloor(n-1)/2\rfloor}+1$ 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.

Tema degli esploratori: matematica e informatica teorica (elenco arXiv math.CO, nuovi lavori del giorno).
Categorie arXiv: Group Theory (math.GR) ; Combinatorics (math.CO).
Pagina del lavoro: https://arxiv.org/abs/2610.22388 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-19T09:34:59.756Z dalla pagina https://arxiv.org/list/math.CO/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).