11.125 (1990)

Let $G$ be a finite group admitting a regular elementary abelian group of automorphisms $V$ of order $p^n$. Is it true that the subgroup $H = \bigcap_{v \in V \setminus \{1\}} [G, v]$ is nilpotent? In the case of an affirmative answer, does there exist a function depending only on $p$, $n$, and the derived length of $G$ which bounds the nilpotency class of $H$?