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edited May 10, 2015 at 17:01

Let $G$ be a (countable) residually finite group whose profinite completion is topologically finitely generated. Must $G$ be finitely generated?

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edited May 10, 2015 at 16:38

Finite generation and profiiteprofinite completion

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asked May 10, 2015 at 16:32

Finite generation and profiite completion

Let $G$ be a residually finite group whose profinite completion is topologically finitely generated. Must $G$ be finitely generated?