Let $G=\langle x,y\mid x^2=y^2\rangle$, prove that exists subgroup of $G$ with index $2$.
Prove that group $G$ has subgroup with index 2
3
$\begingroup$
group-theory
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4@Mariano: It says so. – 2012-12-12
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0yes, this is my homework and i have no idea to prove that – 2012-12-12
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0What does $G=
$ mean ? – 2012-12-12 -
0Perhaps $G=
$ means the group generated by $x,y$ with the single relation $x^2=y^2$. – 2012-12-12 -
0This group is also solvable, interesting, and also torsion free – 2015-05-28