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).