J Austral Math Soc Ser A 53 pp338--351, 1992.

Maximal Subgroups of Infiite Dimensional General Linear Groups

Dugald MacPherson

Abstract

Let k be an infinite cardinal, F a field, and let GL(k, F) be the groups of all non-singular linear transformations on a k-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 folters or ideals on a set, (ii) almost stabilizers of zertain 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.

1991 AMS Subject Classification: 20B07

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Authors

Dugald MacPherson

School of Mathematical Sciences, Queen Mary and Westfield College, Mile End Road, London E1 4NS, England.