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Let $G=$. Consider a homomorphism $\phi$ from $G$ to $$ where $\phi(a)=c^2$ and $\phi(b)=c$. Can someone help me decide what group the kernel of this map is? Thanks!

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    The group can be written as a nice semidirect product, see here: http://math.stackexchange.com/questions/17412/can-someone-tell-me-what-group-this-is/17471#174712011-02-10
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    In particular the kernel is the infinite dihedral group, generated by $ab^{-2}$ and $bab^{-3}$.2011-02-10

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