On certain groups with $G$-contrainvariant subspaces

Abstract

For the field 𝔽 and 𝔽-vector space A, let G be a subgroup of GL(𝔽,A), the group of invertible 𝔽-linear transformations of A. A subspace B of A is G-contrainvariant if GB=A. We discuss groups G and vector spaces A such that every subspace of A is either G-invariant or G-contrainvariant.