15.52 (2002)

By a famous theorem of Wielandt the sequence $G_0 = G, G_1, \dots$, where $G_{i+1} = \text{Aut}\,G_i$, stabilizes for any finite group $G$ with trivial centre. Does there exist a function $f$ of natural argument such that $|G_i| \leqslant f(|G|)$ for all $i = 0, 1, \dots$ for an arbitrary finite group $G$ and the same kind of sequence?