On the conjugacy problem for subdirect products of hyperbolic groups

Martin R. Bridson

paper

On the conjugacy problem for subdirect products of hyperbolic groups

arXiv:2507.05087

Abstract

If $G_{1}$ and $G_{2}$ are torsion-free hyperbolic groups and $P < G_{1} \times G_{2}$ is a finitely generated subdirect product, then the conjugacy problem in $P$ is solvable if and only if there is a uniform algorithm to decide membership of the cyclic subgroups in the finitely presented group $G_{1} / (P \cap G_{1})$ . The proof of this result relies on a new technique for perturbing elements in a hyperbolic group to ensure that they are not proper powers.

Final accepted version, to be published in Mathematische Annalen. 18 pages, 7 figures