The conjugacy problem in finitely generated subdirect products of torsion-free hyperbolic groups is solvable if and only if cyclic subgroup membership is uniformly decidable in G1/(P ∩ G1).
Bridson, Conjugacy in fibre products, distortion, and the geometry of cyclic subgroups , preprint, Stanford, April 2025
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On the conjugacy problem for subdirect products of hyperbolic groups
The conjugacy problem in finitely generated subdirect products of torsion-free hyperbolic groups is solvable if and only if cyclic subgroup membership is uniformly decidable in G1/(P ∩ G1).