Definition: A group $\displaystyle G$ is calledhopfianif every surjective homomorphism $\displaystyle G \longrightarrow G$ is injective. Clearly every finite group is hopfian.

Problem: Prove that $\displaystyle G=<x,y: \ \ y^{-1}x^2y=x^3>$ isnothopfian.

Suggestion:Spoiler: