Abstract A generating set for a finite group G is minimal if no proper subset generates , and $m(G)$ denotes the maximal size of . We prove conjecture Lucchini, Moscatiello Spiga by showing that there exist $a,b> 0$ such any satisfies $m(G) \leqslant \cdot \delta (G)^b$ $\delta (G) = \sum _{p \text { prime}} m(G_p)$ where $G_p$ Sylow p -subgroup To do this, we first bound all almost simple g...