On the conjugacy problem for subdirect products of hyperbolic groups
Abstract
Abstract If $$G_1$$ G 1 and $$G_2$$ G 2 are torsion-free hyperbolic groups and $$P P < G 1 × G 2 is a finitely generated subdirect product, then the conjugacy problem in P is solvable if and only if there is a uniform algorithm to decide membership of the cyclic subgroups in the finitely presented group $$G_1/(P\cap G_1)$$ G 1 / ( P ∩ 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.
Fields of Study & Subjects
Geometric and Algebraic Topology
Publication details
- Journal / source
- Mathematische Annalen
- Volume
- 395
- Issue
- 2
- Publication date
- 5 May 2026
- Language
- EN