nLab Baumslag-Solitar group

Baumslag–Solitar group $BS(m,n)$ for $m,n\neq 0$ is usually defined via its presentation

$$BS(m,n) = \langle x,y \mid x^{-1} y^m x = y^n \rangle$$

This series of groups appears often in combinatorial group theory and geometric group theory. The simplest case $BS(1,1)$ is clearly isomorphic to $\mathbf{Z}\times\mathbf{Z}$.