Generation by Conjugate Elements of Finite Almost Simple Groups With a Sporadic Socle

Abstract

We study the minimum number of elements in the conjugacy class of an automorphism of a sporadic simple group that generate a subgroup containing all inner automorphisms. These results refine the estimates obtained earlier in the papers by Guralnick and Saxl and by Di Martino, Pellegrini, and Zalesski.

Keywords

• sporadic group
• fischer group
• conjugacy
• generators
• baer–suzuki theorem