# Free groups and homomorphisms

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• April 14th 2012, 12:12 PM
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.