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If $G$ is a free group on $n>1$ generators, then $[G,G]$ is also free, being a subgroup of a free group. Is there a formula for the number of generators of this free group in terms of n?

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closed as too localized by Ryan Budney, Ian Agol, Fernando Muro, Andreas Blass, Qiaochu Yuan Aug 19 '12 at 2:37

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Yes, it's infinite. –  Ryan Budney Aug 18 '12 at 22:38
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It's infinite. One way to see this is to write down the corresponding covering space of the wedge of $n$ circles and note that it is homotopy equivalent to a wedge of infinitely many circles. –  Qiaochu Yuan Aug 18 '12 at 22:48
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