5.26 (1976)

Let $G$ be a finite $p$-group with the minimal number of generators $d$, and let $r_1$ (respectively, $r_2$) be the minimal number of defining relations on $d$ generators in the sense of representing $G$ as a factor-group of a free discrete group (pro-$p$-group). It is well known that always $r_2 > d^2/4$. For each prime number $p$ denote by $c(p)$ the exact upper bound for the numbers $b(p)$ with the property that $r_2 \geqslant b(p)d^2$ for all finite $p$-groups.
$\qquad$ a) It is obvious that $r_1 \geqslant r_2$. Find a $p$-group with $r_1 > r_2$.
$\qquad$ b) Conjecture: $\lim\limits_{p \to \infty} c(p) = 1/4$.