Let $G$ be a finitely generated group and $\varphi:G\to \operatorname{Aut}(\mathbb C)$ a homomorphism, where $\operatorname{Aut}(\mathbb C)$ is the group of complex affine transfromations $a z+b$.

Can we find a torsion free-subgroup $H$ of $G$ with finite index? And can we find a normal subgroup $H$ which is torsion-free with finite index?

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