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Assume that a finite group $G$ has a family of $d$-generator subgroups whose indices have no common divisor. Is it true that $G$ can be generated by $d+1$ elements?

Contributor: A. Lucchini

Progress

The answer is positive if $G$ is solvable (L. G. Kovács, H.-S. Sim, Indag. Math., 2 (1991), 229–232). For an arbitrary finite group $G$ it is proved that $G$ can be generated by $d+2$ elements (A. Lucchini, Commun. Algebra, 28, no. 4 (2000), 1875–1880).

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