The socle of a projective Mackey functor for a p-group

We study the simple subfunctors of indecomposable projective Mackey functors for a p-group P. Unlike the case of group algebras, the Mackey algebra is not in general self-injective. Thus, the socle of an indecomposable projective functor is not in general simple. We first show that the simple subfunctors of a projective functor P_{H,k}, where H