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Maximal subgroups of infinite dimensional general linear groups

Part of: Permutation groups

Published online by Cambridge University Press:  09 April 2009

Dugald Macpherson
Dugald Macpherson
Affiliation:
School of Mathematical Sciences Queen Mary and Westfield CollegeMile End RoadLondon E1 4NS, England
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Abstract

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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.

MSC classification

Secondary: 20B07: General theory for infinite groups
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 53 , Issue 3 , December 1992 , pp. 338 - 351
Copyright
Copyright © Australian Mathematical Society 1992

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