Extremal and maximal normal abelian subgroups of a maximal unipotent subgroup in groups of Lie type

被引：13

作者：

Levchuk, Vladimir M. ^{[1
]}

Suleimanova, Galina S. ^{[1
]}

机构：

[1] Siberian Fed Univ, Inst Math, Krasnoyarsk 660041, Russia

来源：

JOURNAL OF ALGEBRA | 2012年 / 349卷 / 01期

基金：

俄罗斯基础研究基金会;

关键词：

Group of Lie type; Unipotent subgroup; Maximal abelian normal subgroup; Extremal subgroup; Large abelian subgroup;

D O I：

10.1016/j.jalgebra.2011.10.025

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We describe all maximal abelian normal subgroups in the unipotent radical U of a Borel subgroup in a group of Lie type G over a field K. This gives a new description of the extremal subgroups in U which were studied by C. Parker and P. Rowley. For a finite field K, we prove that either each large abelian subgroup in U is G-conjugate to a normal subgroup in U or G is of certain exceptional Lie type. (C) 2011 Elsevier Inc. All rights reserved.

引用

页码：98 / 116

页数：19

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