4.66 (1973)

Let $P$ be a presentation of a finite group $G$ on $m_p$ generators and $r_p$ relations. The deficiency $\operatorname{def}(G)$ is the maximum of $m_p - r_p$ over all presentations $P$. Let $G$ be a finite group such that $G = G' \neq 1$ and the multiplicator $M(G) = 1$. Prove that $\operatorname{def}(G^n) \to -\infty$ as $n \to \infty$, where $G^n$ is the $n$-th direct power of $G$.