A bound on the expected number of random elements to generate a finite group all of whose Sylow subgroups are d-generated

Assume that all the Sylow subgroups of a finite group $G$ can be generated by $d$ elements. Then the expected number of elements of $G$ which have to be drawn at random, with replacement, before a set of generators is found, is at most $d+η$ with $η\sim 2.875065.$

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