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.

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