Algebraic groups and automorphisms of finite simple Chevalley groups

Abstract

Using the vanishing of Galois cohomology of algebraic groups defined over finite fields, due to S. Lang, we further our study of the splitting properties of the automorphism groups of finite Chevalley groups. We show that under suitable restrictions on the base fields there are no complements for the inner automorphism groups in the automorphism groups of Chevalley groups. The results are somewhat complementary to the author's work on the same problem, in another paper.