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.

Location: http://mech.math.msu.su/~fpm/eng/k13/k131/k13105h.htm

Last modified: September 5, 2013