Baumslag-Solitar group

Definition
Suppose $$m,n$$ are integers. The Baumslag-Solitar group $$BS(m,n)$$ is defined as a group with the following presentation:

$$\! BS(m,n) := \langle a,b \mid ba^mb^{-1} = a^n \rangle$$

Note that $$BS(m,n) \cong BS(n,m)$$ by identifying the $$b$$ of the first group with the $$b^{-1}$$ f the second. Also, $$BS(m,n) \cong BS(-m,-n)$$, so it suffices to consider pairs where at least one element is nonnegative.