MathOverflow is a question and answer site for professional mathematicians. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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?

share|cite|improve this question

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

This question is unlikely to help any future visitors; it is only relevant to a small geographic area, a specific moment in time, or an extraordinarily narrow situation that is not generally applicable to the worldwide audience of the internet. For help making this question more broadly applicable, visit the help center.If this question can be reworded to fit the rules in the help center, please edit the question.

Yes, it's infinite. – Ryan Budney Aug 18 '12 at 22:38
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