Suppose are integers. The Baumslag-Solitar group is defined as a group with the following presentation:
Note that by identifying the of the first group with the f the second. Also, , so it suffices to consider pairs where at least one element is nonnegative.
|What group do we get?|
|1||1||free abelian group of rank two|
|1||-1||fundamental group of Klein bottle|