3 papers
math.GR2025
First-order theory of torsion-free Tarski monsters
Rémi Coulon, Francesco Fournier-Facio, Meng-Che "Turbo" Ho
We develop methods to control the first-order theory of groups arising as certain direct limits of torsion-free hyperbolic groups, answering several questions in the literature. We…
math.GR2025
Power quotients of surface groups and mapping class groups
Rémi Coulon, Alessandro Sisto, Henry Wilton
Let be the fundamental group of a closed, orientable, hyperbolic surface . The -power quotient, , is the quotient of by the th powers of simple closed cur…
math.GR2024
Infinite simple characteristic quotients
Rémi Coulon, Francesco Fournier-Facio
We construct continuum many infinite, simple, characteristic quotients of non-abelian free groups, answering a 1978 question of James Wiegold. The method is very flexible, allowing…