14.15 (1999)

For the automorphism group $A_n = \operatorname{Aut} F_n$ of a free group $F_n$ of rank $n \geqslant 3$ find the supremum $k_n$ of the commutator lengths of the elements of $A'_n$.

It is easy to show that $k_2 = \infty$. On the other hand, the commutator length of any element of the derived subgroup of $\varinjlim A_n$ is at most 2 (R. K. Dennis, L. N. Vaserstein, K-Theory, 2, N 6 (1989), 761–767).