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math.GR2026
On the measure of definable sets in profinite groups
Martina Conte, Matteo Vannacci
We study the (Haar) measure of verbal sets in profinite groups, and especially in free profinite groups. Relating the measure of a verbal set with the width of the corresponding wo…
math.GR2026
Concise formulae in groups of non-positive curvature
Laura Ciobanu, Martina Conte
We show that first-order formulae are concise in acylindrically hyperbolic groups and certain extensions thereof. We study further classes of groups, including Burnside groups, icc…