FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2013, VOLUME 18, NUMBER 1, PAGES 57-62

Normalizers of Chevalley groups of type $G$₂ over local rings without $1/2$

E. I. Bunina
P. A. Veryovkin

Abstract

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In this paper, we prove that every element of the linear group $GL$₁₄(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.

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Last modified: September 5, 2013