Concise formulae in groups of non-positive curvature

Abstract

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 groups, groups with the `Big Powers' condition, torus knot groups and more, and prove conciseness for wide classes of formulae. We also explore properties of definable sets in these groups, such as their finiteness, depending on the type of formula considered.