FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2011/2012, VOLUME 17, NUMBER 1, PAGES 155-168

The normal structure of the unipotent subgroup in Lie type groups and its extremal subgroups

V. M. Levchuk
G. S. Suleimanova

Abstract

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We study the normal structure of the unipotent radical $U$ of a Borel subgroup in a Lie type group over a field $K$. Thus, all maximal Abelian normal subgroups in $U$ are described. This gives a new solution of C. Parker and P. Rowley's problem about extremal subgroups in $U$ and the description in finite groups $U$ of the large normal (and, as proved, also normal large) Abelian subgroups.

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Last modified: January 31, 2012