On the conjugacy problem for subdirect products of hyperbolic groups

Martin R. Bridson

On the conjugacy problem for subdirect products of hyperbolic groups

Group Theory 2026-04-14 v2

Authors: Martin R. Bridson

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.

Keywords

conjugacy problem hyperbolic groups subdirect products torsion-free cyclic subgroups finitely presented groups

Cite

@article{arxiv.2507.05087,
  title  = {On the conjugacy problem for subdirect products of hyperbolic groups},
  author = {Martin R. Bridson},
  journal= {arXiv preprint arXiv:2507.05087},
  year   = {2026}
}

Comments

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

On the conjugacy problem for subdirect products of hyperbolic groups

Abstract

Keywords

Cite

Comments

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