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Let $G$ be a fully residually free group with a finitely generated profinite completion. Is $G$ necessarily finitely generated?

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    $\begingroup$ I don't think the tag logic is relevant. On the other hand I was wondering if one could replace "f.g. profinite completion" by something even weaker such as "$G/[G,G]G^2$ is finite". $\endgroup$
    – YCor
    Commented Nov 24, 2015 at 13:02

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