12.71 (1992)

Let $d(G)$ denote the smallest cardinality of a generating set of the group $G$. Let $A$ and $B$ be finite groups. Is there a finite group $G$ such that $A, B \leqslant G$, $G = \langle A, B \,\rangle$, and $d(G) = d(A)+d(B)$? The corresponding question has negative answer in the class of solvable groups (L. G. Kovács, H.-S. Sim, Indag. Math., 2, no. 2 (1991), 229–232).