On the conjugacy problem for subdirect products of hyperbolic groups

Journal article

Abstract:: If G₁ and G₂ are torsion-free hyperbolic groups and P < G₁ × G₂ 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 G₁/(P ∩ G₁). 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.

Files:: Bridson_2026_On_the_conjugacy.pdf

(Preview, Version of record, pdf, 496.3KB, Terms of use)

Language:: English
Keywords:: subdirect products

conjugacy problem

hyperbolic groups

rel-cyclics Dehn function
Pubs id:: 2404552
Local pid:: pubs:2404552
Deposit date:: 2026-04-10
ARK identifier:: ark:/29072/ora_44a724a01a41427c88b5dcd52d5da1c0

Copyright holder:: Martin R. Bridson
Rights statement:: © The Author(s) 2026. Open Access. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.

If you are the owner of this record, you can report an update to it here: Report update to this record