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Infinite dimensional linear groups with a spacious family of G-invariant subspaces

Author A. V. Sadovnichenko
sadovnichenko.lit@rambler.ru
Oles Honchar Dnipropetrovsk National University

Abstract Let F be a field, A be a vector space over F, GL(F,A) be the group of all automorphisms of the vector space A. If B≤A then denote by Core the largest G-invariant subspace of B. A subspace B is called almost G-invariant if \mathop{\rm dim}_F (B/\mathop{\rm Core}_G (B)) is finite. In this paper we described the {case where} every subspace of A is almost G-invariant.
Keywords vector space; linear group; module; G-invariant subspace; almost invariant subspace
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Pages 11-15
Volume 40
Issue 1
Year 2013
Journal Matematychni Studii
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