Fundamental group of Klein bottle

Definition
The fundamental group of Klein bottle is defined in the following equivalent ways:


 * 1) It is the defining ingredient::fundamental group of the Klein bottle.
 * 2) It is the defining ingredient::Baumslag-Solitar group $$BS(1,-1)$$.
 * 3) It is given by the presentation:

$$\langle a,b \mid bab^{-1} = a^{-1} \rangle$$

Note that the group admits the infinite dihedral group as a quotient group.