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Could anyone give me a suggestion to solve this problem about group presentations?

Show that the class of the word $aba$ in group $\langle{a,b\mid a^{2}b^{2} }\rangle$ is not the trivial element.

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closed as off-topic by Shaun, Aweygan, user99914, Leucippus, JonMark Perry Oct 14 '17 at 6:00

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There is a homomorphism from your group to the cyclic group of order 2 which maps the two generators to the nonzero element and aba to a nonzero element.

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As a matter of strategy, try to find some abelian quotient in which $2a + b \ne 0$ (using additive notation). Note (in your quotient) $2a + b = -b$. So now it suffices to find an abelian quotient in which $b \ne 0$.

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