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16.53 (2006)

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Let $d(G)$ denote the smallest cardinality of a generating set of the group $G$. Suppose that $G = \langle A, B \rangle$, where $A$ and $B$ are two $d$-generated finite groups of coprime orders. Is it true that $d(G) \leqslant d + 1$? See 12.71 and (A. Lucchini, J. Algebra, 245 (2001), 552–561).

Contributor: A. Lucchini

Progress

Comment of 2021: the answer is yes if $A$ and $B$ have prime power order (E. Detomi, A. Lucchini, J. London Math. Soc. (2), 87, no. 3 (2013), 689–706).

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