On automorphisms of finite simple Chevalley groups

Abstract

The paper deals with the splitting properties of the automorphism groups of finite Chevalley groups. Using the action of symmetries of a Dynkin diagram on the corresponding Weyl group, a sufficient condition is developed for the existence of a complement for the inner automorphism group in the automor ph-ism group of a finite Chevalley group. The condition is verified for Chevalley groups of the classical types (viz., the group of type A l , B l , C l ,and D l ) as well as the exceptional groups of type E 6 and E 7, under suitable restrictions on the base fields.