There exist maximal class groups of arbitrarily large derived length

Statement

Let $\ell$ be a positive integer. It is possible to find a prime number $p$ and a finite p-group $P$ such that:

• $P$ is a maximal class group.
• The derived length of $P$ is at least $\ell$.

Proof

The idea of the proof is to use the Panferov Lie group: the Lazard Lie group (via the Lazard correspondence) of the Panferov Lie algebra for a sufficiently large prime $p$ (choose $p$ as a prime greater than $2^{\ell +1}-2$ -- for more, see the derived length computation for Panferov Lie algebra#Arithmetic functions).