# Free groups and homomorphisms

• Apr 14th 2012, 11:12 AM
kierkegaard
Free groups and homomorphisms
Consider the group $G=\mathbb{Z}_2\ast\mathbb{Z}_3=$ and consider the surjective homomorphisms $G\twoheadrightarrow\mathbb{Z}_2$, $G\twoheadrightarrow\mathbb{Z}_3$ and $G\twoheadrightarrow\mathbb{Z}_6$. Find a presentation and the abelianization of each kernel.