On the conjugacy problem for subdirect products of hyperbolic groups

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2026年5月5日

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Martin R. Bridson

摘要

If $G_1$ $G_{1}$ and $G_2$ $G_{2}$ are torsion-free hyperbolic groups and $P<G_1\times G_2$ $P < G_{1} \times G_{2}$ 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 $G_1/(P\cap G_1)$ $G_{1} / (P \cap G_{1})$ . 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.