Automorphisms and isomorphisms of Chevalley groups of type $G_2$ over local rings with 1/2 and 1/3

Abstract

We prove that every isomorphism of Chevalley groups of type $G_2$ over commutative local rings with 1/2 and 1/3 is standard, i. e., it is a composition of a ring isomorphism and an inner automorphism.