Let G be the group defined by generators a,b and relations $a^4=e$, $a^2b^{-2}=e$, $abab^{-1}=e$. Since the quaternion group of order 8 is generated by elements $a,b$ satisfying the previous relations, there is an epimorphism from $G$ onto $Q_8$. Let $F$ be the free group on $\{a,b\}$ and $N$ the normal subgroup generated by $\{ a^4, a^2b^{-2}, abab^{-1} \}$. How to write down the normal subgroup N and express the group F/N ?
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