On the conjugacy problem for subdirect products of hyperbolic groups
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866910121506897920 |
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| author | Bridson, Martin R. |
| author_facet | Bridson, Martin R. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_05087 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the conjugacy problem for subdirect products of hyperbolic groups Bridson, Martin R. Group Theory 20F67, 20F10, 20F65 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. |
| title | On the conjugacy problem for subdirect products of hyperbolic groups |
| topic | Group Theory 20F67, 20F10, 20F65 |
| url | https://arxiv.org/abs/2507.05087 |