A probabilistic version of a theorem of lászló kovács and hyo-seob sim

For a finite group group, denote by V(G) the smallest positive integer k with the property that the probability of generating G by k randomly chosen elements is at least 1/e. Let G be a finite soluble group. {Assume} that for every p∈π(G) there exists Gp≤G such that p does not divide |G:Gp| and V(Gp)≤d. Then V(G)≤d+7.