PreprintCC BY 4.0arXiv
Eventual Exactness and Rigidity for Abelian Covers of Groups
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 supω(G)≤ na(G)=2⌊(n−1)/2⌋+1 for every n≥ 63. Equality holds precisely for groups with derived subgroup of order two and binary symplectic central quotient of dimension 2⌊(n−1)/2⌋. The proof combines centralizer descent with a structural separation of nonscalar alternating commutator maps.
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BibTeX
@misc{lecomte2026eventual,
title = {{Eventual Exactness and Rigidity for Abelian Covers of Groups}},
author = {Guillaume Lecomte},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.22388},
eprint = {2610.22388},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.22388},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Eventual Exactness and Rigidity for Abelian Covers of Groups
AU - Guillaume Lecomte
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.22388
UR - https://arxiv.org/abs/2610.22388
AB - 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)≤ na(G)=2^⌊(n−1)/2⌋+1 for every n≥ 63. Equality holds precisely for groups with derived subgroup of order two and binary symplectic central quotient of dimension 2⌊(n−1)/2⌋. The proof combines centralizer descent with a structural separation of nonscalar alternating commutator maps.
ER -