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edited Nov 23, 2015 at 6:27

Let $G$ be a Fuchsian group whose profinite completion is finitely generated. Must $G$ be finitely generated?

A Fuchsian group is a discrete subgroup of $\mathrm{SL}_2(\mathbb{R})$ or $\mathrm{PSL}_2(\mathbb{R})$.

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asked Nov 23, 2015 at 6:22

Profinite rank of Fuchsian groups

Let $G$ be a Fuchsian group whose profinite completion is finitely generated. Must $G$ be finitely generated?