On the number of generators of a finite group (Q5903357)

In 1968 L. G. Kovács proved that a finite soluble group can be generated by \(d+1\) elements if each of its Sylow subgroups can be generated by d elements. The purpose of this paper is to prove a result of the same kind for arbitrary finite groups: Theorem. Let G be a finite group. If every Sylow subgroup of G can be generated by d elements, then G can be generated by 2d elements. The proof uses the classification of the finite simple groups.