On some linear groups, having a big family of G-invariant subspaces - Kurdachenko, L.A.; Sadovnichenko, A.V. (Algebra and Discrete Mathematics, 2013)
Let F be a field, A a vector space over F, GL(F, A) be the group of all automorphisms of the vector space A. If B is a subspace of A, then denote by BFG the G-invariant subspace, generated by B. A subspace B is called nearly G-invariant, if dimF(BFG/B) is finite. In this paper we described the situation when every subspace of A is nearly G-invariant.