FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2009, VOLUME 15, NUMBER 7, PAGES 205-216

**On a conjugacy in a Chevalley group of large Abelian
subgroups of the unipotent subgroup**

G. S. Suleimanova

Abstract

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Let $U$ be the
unipotent subgroup of a Chevalley group over a finite field.
The well-known problem about describing the set of "large" (of maximal
order) Abelian subgroups in $U$ of exceptional type is
investigated.
The description of normal large Abelian subgroups in $U$ was established earlier.
It is proved that each large Abelian subgroup from $U$ is conjugate in the
Chevalley group of type $F$_{4} over
a finite field of characteristic not equal to $2$ to a normal subgroup
in $U$.
It is shown that for the groups $U$ of type $G$_{2}
and $3D$_{4}
the similar conclusion is not true.

Location: http://mech.math.msu.su/~fpm/eng/k09/k097/k09710h.htm

Last modified: April 18, 2010