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

被引：0
作者：
V. M. Levchuk
G. S. Suleimanova
机构：
[1] Siberian Federal University, Krasnoyarsk
[2] Khakas Technical Institute of Siberian Federal University, Abakan
来源：
Journal of Mathematical Sciences | 2012年 / 185卷 / 3期
基金：
俄罗斯基础研究基金会;
关键词：
Normal Subgroup; Abelian Subgroup; Chevalley Group; Borel Subgroup; Root Element;
D O I：
10.1007/s10958-012-0927-8
中图分类号：
学科分类号：
摘要：
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. © 2012 Springer Science+Business Media, Inc.
引用
收藏
页码：448 / 457
页数：9
相关论文
共 35 条
  • [1] Barry M.J.J., Large Abelian subgroups of Chevalley groups, J. Aust. Math. Soc. Ser. A, 27, 1, pp. 59-87, (1979)
  • [2] Barry M.J.J., Wong W.J., Abelian 2-subgroups of finite symplectic groups in characteristic 2, J. Aust. Math. Soc. Ser. A, 33, 3, pp. 345-350, (1982)
  • [3] Bourbaki N., Groupes et algebres de Lie, (1968)
  • [4] Carter R., Simple Groups of Lie Type, (1972)
  • [5] Gibbs J., Automorphisms of certain unipotent groups, J. Algebra, 14, 2, pp. 203-228, (1970)
  • [6] Gupta C.K., Levchuk V.M., Ushakov Y.Y., Hypercentral and monic automorphisms of classical algebras, rings and groups, J. Sib. Fed. Univ., Math. Phys., 1, 4, pp. 380-390, (2008)
  • [7] Kondrat'ev S., Subgroups of finite Chevalley groups, Usp. Mat. Nauk, 41, 247, pp. 57-96, (1986)
  • [8] Kuzucuoglu F., Levchuk V.M., The automorphism group of certain radical rings, J. Algebra, 243, pp. 473-485, (2001)
  • [9] Kuzucuoglu F., Levchuk V.M., Isomorphism of certain locally nilpotent finitary groups and associated rings, Acta Appl. Math., 82, 2, pp. 169-181, (2004)
  • [10] Levchuk V.M., Relation of the unitriangle group to certain rings, Algebra Logic, 15, 5, pp. 348-360, (1976)
1234