Automorphisms of a Chevalley group of type G₂ over a commutative ring R with 1/3 generated by the all invertible elements and 2R

2023/07/24 by Bunina, Elena, Vladykina, Maria
#20G35 #FOS: Mathematics #Group Theory (math.GR) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2307.12920

Abstract

In this paper we prove that every automorphism of a Chevalley group with the root system G₂ over a commutative ring R with 1/3, generated by all its invertible elements and the ideal 2R is a composition of ring and inner automorphisms.

Related

• Automorphisms of Chevalley groups over commutative rings
• Automorphisms of Chevalley groups of different types over commutative rings
• Automorphisms and isomorphisms of Chevalley groups of type G₂ over local rings with 1/2 and 1/3
• Automorphisms of Chevalley groups of types B₂ and G₂ over local rings
• Automorphisms of elementary adjoint Chevalley groups of types A_l, D_l, E_l over local rings with 1/2