  Denote by $m(G)$ the largest size of a minimal generating set of a finite
group $G$. We estimate $m(G)$ in terms of $\sum_{p\in \pi(G)}d_p(G),$ where we
are denoting by $d_p(G)$ the minimal number of generators of a Sylow
$p$-subgroup of $G$ and by $\pi(G)$ the set of prime numbers dividing the order
of $G$.
