p-local module

A p-local module here is a finite direct sum of induced representations from normalizers $N_G(Q)$ of nontrivial p-subgroups $Q$. This usage includes induction from $G$ itself when $G$ normalizes such a subgroup. Green correspondence and induction on vertex order express every finite module, or lattice over a complete valuation ring, as a difference of p-local modules after adjoining projective modules.