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

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 $B \leq A$ then denote by $\mathop{\rm Core}_G (B)$ 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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