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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