Maximal subgroups of infinite dimensional general linear groups
1992 ◽
Vol 53
(3)
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pp. 338-351
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Keyword(s):
AbstractLet 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.
2004 ◽
Vol 134
(3)
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pp. 477-499
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1994 ◽
Vol 124
(6)
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pp. 1135-1150
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Keyword(s):
2017 ◽
Vol 83
(12)
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pp. 83-111
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Keyword(s):