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

Abstract

For a finite group group‎, ‎denote by $\mathcal V(G)$ 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 $p\in \pi(G)$ there exists $G_p\leq G$ such that $p$ does not divide $|G:G_p|$ and ${\mathcal V}(G_p)\leq d.$ Then ${\mathcal V}(G)\leq d+7.$‎

Keywords

• ‎‎‎finite soluble groups
• generation of finite groups