Comparing the order and the minimal number of generators of a finite irreducible linear group
Derek F. Holt, Gareth Tracey · arXiv (Cornell University) · 2021
We prove that $d(G) \log |G| = O(n^2 \log q)$ for irreducible subgroups $G$ of GL$(n,q)$, and estimate the associated constants. The result is motivated by attempts to bound the complexity of computing the automorphism groups of various classes of finite groups.