Generators for finite groups with a unique minimal normal subgroup (Q1378843)

The authors prove that, if \(G\) is a finite group having a unique minimal normal subgroup \(N\), then the number of elements needed to generate \(G\) is not more than the number needed to generate \(G/N\) (assuming the latter number is at least two). The proof depends on the classification of finite simple groups, and about half of the paper is occupied with proving a lemma about outer automorphisms of non-abelian finite simple groups by considering various cases.