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Non-residually Finite Groups Hyperbolic Relative to Residually Finite Subgroups by Kim, Jan; Lee, Donghi is a scholarly article available to read on EtoBox.

What is Non-residually Finite Groups Hyperbolic Relative to Residually Finite Subgroups about?

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.

Author

Kim, Jan; Lee, Donghi

Published

2019

Language

EN