Linear transvection groups and embedded polar spaces

• 成果类型: Article
• 署名作者: Cuypers, H; Steinbach, A
• 署名单位: Eindhoven University of Technology; Justus Liebig University Giessen
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s002220050328
• 发表日期: 1999
• 页码: 169-198
• 关键词: root elements; SUBGROUPS; MODULES

摘要

Most classical groups arising from (anti-) hermitian forms or (pseudo-) quadratic forms contain so-called isotropic transvections. The isotropic transvection subgroups of these classical groups, i.e., the subgroups generated by all isotropic transvections with a fixed axis, form a class Sigma of abelian subgroups which is a class of abstract transvection groups in the sense of Timmesfeld [24]. In this paper we give a common characterization of all these classical groups with isotropic transvections as linear groups generated by a class Sigma of abstract transvection groups such that the elements of A is an element of C are transvections.