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Let $G=\langle x,y\mid x^2=y^2\rangle$, prove that exists subgroup of $G$ with index $2$.

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    @Mariano: It says so.2012-12-12
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    yes, this is my homework and i have no idea to prove that2012-12-12
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    What does $G=$ mean ?2012-12-12
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    Perhaps $G=$ means the group generated by $x,y$ with the single relation $x^2=y^2$.2012-12-12
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    This group is also solvable, interesting, and also torsion free2015-05-28

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