Author

Guillaume Lecomte

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Preprint Oct 2026

Eventual Exactness and Rigidity for Abelian Covers of Groups

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 subg...

Guillaume Lecomte · 0 citations

Preprint Aug 2026

Sharp Asymptotics for Abelian Covers of Groups with Bounded Noncommutativity

We determine the sharp exponential growth rate of the minimum number of abelian subgroups required to cover a group with bounded pairwise noncommutativity. Let $\omega(G)$ denote the largest size of a pairwise noncommuting subset of a group $G$, let $a(G)$ be the least size of an abelian cover, and define $h(n)=\sup\{a...

Guillaume Lecomte · 0 citations