14.24 (1999)

Let $\operatorname{Aut} F_n$ be the automorphism group of a free group of rank $n$ with norm $\lVert \cdot \rVert$ as in 14.23. Does there exist a recursive function $f : \mathbb{N} \times \mathbb{N} \to \mathbb{N}$ with the following property: for any two conjugate elements $\alpha, \beta \in \operatorname{Aut} F_n$ there is an element $\gamma \in \operatorname{Aut} F_n$ such that $\gamma^{-1}\alpha\gamma = \beta$ and $\lVert \gamma \rVert \leqslant f(\lVert \alpha \rVert, \lVert \beta \rVert)$?