Maximal subgroups of infinite dimensional general linear groups

Journal of the Australian Mathematical Society

Dugald Macpherson¹ 

关键词: 20 B 07;   

DOI  :  10.1017/S144678870003651X

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

Let k be an infinite cardinal, F a field, and let GL(k, F) be the group of all non-singular linear transformations on a ki-dimensional vector space V over F. Various examples are given of maximal subgroups of GL(k, F). These include (i) stabilizers of families of subspaces of V which are like filters or ideals on a set, (ii) almost stabilizers of certain subspaces of V, (iii) almost stabilizers of a direct decomposition of V into two k-dimensional subspaces.It is also noted that GL(k, F) is not the union of any chain of length k of proper subgroups.

【 授权许可】

Unknown