On same-invariant linear groups

A linear group $G\le\operatorname{GL}(V)$ is called same-invariant if the subspaces of linear invariants $V^g$ are the same for all $g\in G$, $g\ne 1$. In this paper, we consider finite same-invariant linear groups over а field of characteristic $p$ which have order $p^2$ or $pq$, $(p,q)=1$.