Not a Hopfian group
Posted: Sun Jun 11, 2017 9:20 pm
Definition: A group is called hopfian if every surjective homomorphism $f: \mathcal{G} \rightarrow \mathcal{G}$ is an isomorphism. Clearly every finite group is hopfian.
Problem:
Prove that
\[\mathcal{G} = \langle x, y: y^{-1} x^2 y = x^3 \rangle\]
is not hopfian.
Problem:
Prove that
\[\mathcal{G} = \langle x, y: y^{-1} x^2 y = x^3 \rangle\]
is not hopfian.