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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.22841 |
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Table of Contents:
- We exhibit examples of finitely presented subgroups $P$ of direct products of hyperbolic groups for which there is no algorithm that detects whether a finitely presented group has a quotient isomorphic to $P$. For any torsion-free, linear, hyperbolic group $Q$ that maps onto the free group of rank $2$ and $m\geq 2$, we construct a recursive sequence $(Γ_n)_{n\in \mathbb{N}}$ of torsion-free, hyperbolic $C'(\frac{1}{6})$ small cancellation groups, with the property that there is no algorithm determining the values $n\in \mathbb{N}$ such that $Γ_n$ has a quotient isomorphic to the direct product $Q^{m}$ of $m$-copies of $Q$.