Bounding the maximal size of independent generating sets of finite groups

Abstract

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 $G$.

11 pages