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.
A probabilistic version of a theorem of Laszlo Kovacs and Hyo-Seob Sim
Lucchini A.
;Moscatiello M.
2020
Abstract
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.
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