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

TL;DR

This paper proves that all isomorphisms of Chevalley groups of type G_2 over certain local rings are standard, composed of ring isomorphisms and inner automorphisms, clarifying their structure.

Contribution

It establishes that all group isomorphisms for G_2 Chevalley groups over specified local rings are standard, extending understanding of their automorphism structure.

Findings

All isomorphisms are standard

Automorphisms are compositions of ring isomorphisms and inner automorphisms

Results apply to 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.