Pairs of Short Root Subgroups in the Chevalley Group of Type G2

被引：0

作者：

V. V. Nesterov

机构：

[1] The Baltic State Technical University,

来源：

Journal of Mathematical Sciences | 2004年 / 120卷 / 4期

关键词：

Chevalley Group; Short Root; Root Subgroup; Simultaneous Conjugation; Short Root Subgroup;

D O I：

10.1023/B:JOTH.0000017893.66315.ba

中图分类号：

学科分类号：

摘要：

The paper is devoted to a description of the pairs of unipotent short root subgroups in the Chevalley group of type G2 over a field of characteristic different from 2. Namely, the subgroups generated by a pair of short root subgroups are described, and the orbits of the Chevalley group, which acts by simultaneous conjugation on such pairs, are classified. Most of the calculations are valid for fields of characteristic 2. Bibliography: 14 titles.

引用

页码：1630 / 1641

页数：11

共 13 条

[1] Vavilov N. A.(1988)Geometry of long root subgroups in Chevalley groups Vestn. Leningr. Univ., Mat. 21 5-10
[2] Vavilov N. A.(1989)Mutual arrangement of long and short root subgroups in a Chevalley group Vestn. Leningr. Univ., Mat. 22 1-7
[3] Vavilov N. A.(1990)Subgroups of Chevalley groups containing a maximal torus Trudy Leningr. Mat. Obshch. 1 64-109
[4] Kondrat'ev A. S.(1986)Subgroups of finite Chevalley groups Usp. Mat. Nauk 41 57-90
[5] Nesterov V. V.(1997)Pairs of short root subgroups in a Chevalley group Dokl. Ros. Akad. Nauk 357 302-305
[6] Nesterov V. V.(2000)The arrangement of long and short root subgroups in the Chevalley group of type Zap. Nauchn. Semin. POMI 272 273-285
[7] Aschbacher M.(1976)Involutions in Chevalley groups over fields of even order Nagoya Math. J. 63 1-91
[8] Seitz G. M.(1979)The geometry of root subgroups in exceptional groups Geometria Dedicata 8 317-381
[9] Cooperstein B. N.(1980)Geometry of long root subgroups in groups of Lie type Proc. Symp. Pure Math. 38 243-248
[10] Cooperstein B. N.(1975)Eine endliche Präsentation der Gruppe G Math. Z. 141 243-251

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