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arXiv · 1903.00838

Non-residually finite groups hyperbolic relative to residually finite subgroups

Jan Kim·Donghi Lee
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Abstract

Let $m$ and $k$ be integers such that $|m|, \, |k| >1$ and $\gcd (m,k)=1$. We show that all Baumslag-Solitar groups $BS(m,mk)$ are non-residually finite groups hyperbolic relative to residually finite subgroups. By a result of Osin (2007), this implies that there exists a non-residually finite hyperbolic group, thus solving a long-standing open problem of Gromov (1987). We also show that all $BS(m, mk)$ are non-Hopfian groups hyperbolic relative to Hopfian subgroups.

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Jan Kim, Donghi Lee. 2019-03-03. Non-residually finite groups hyperbolic relative to residually finite subgroups. https://arxiv.org/abs/1903.00838

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