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Given a free group of rank $n$ -> $F_n$ .

Is it easy to see what is the index of the subgroup $ [F_n, F_n ] \subseteq F_n $ ?

Hope someone will be able to help me understand this

Thanks !

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    I think it is infinite index. The commutator subgroup is an infinitely generated (free) group. If it were a finite index subgroup of a finitely generated free group, it too would be finitely generated.2012-07-30
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    The quotient is free abelian of rank $n$, and hence infinite (assuming $n\geq 1$). This is equivalent to saying that the index of the commutator subgroup is infinite.2012-07-30
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    Great! Thanks a lot ! !2012-07-30

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