Normalizers of Chevalley Groups of Type G 2 Over Local Rings Without 1/2

Abstract

In this paper, we prove that every element of the linear group GL14(R) normalizing the Chevalley group of type G 2 over a commutative local ring R without 1/2 belongs to this group up to some multiplier. This allows us to improve our classification of automorphisms of these Chevalley groups showing that an automorphism-conjugation can be replaced by an inner automorphism. Therefore, it is proved that every automorphism of a Chevalley group of type G 2 over a local ring without 1/2 is a composition of a ring and an inner automorphisms.