Let ρ:G→GL(V) be a representation of a finite p-group G over a field of characteristic p. Prove that if the restriction of the linear map ∑g∈Gρ(g) to a finite dimensional subspace W of V is injective, then the subspace spanned by the subspaces ρ(g)W (g∈G) is the direct sum of these subspaces. vectorabstract algebrasuperior algebrasuperior algebra unsolved