4 papers
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…
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…
Conciseness of first-order formulae
Martina Conte, Jan Moritz Petschick
A word is concise in a class of groups if, for every group in , the verbal subgroup is finite whenever takes only finitely many values…
Finite axiomatizability of the rank and the dimension of a pro- group
Martina Conte, Benjamin Klopsch
The Prüfer rank of a profinite group is the supremum, across all open subgroups of , of the minimal number of generators . It is known th…