## 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.