Let G be a finite group, let V be an [ ]G-module of finite dimension d, and denote by β(V, G) the minimal number m such that the invariant ring S(V)G is generated by finitely many elements of degree at most m. A classical result of E. Noether says that β(V, G)[les ][mid ]G[mid ] provided that char [ ] is coprime to [mid ]G[mid ]!. If char [ ] divides [mid ]G[mid ], then no bounds for β(V, G) are known except for very special choices of G. In this paper we present a constructive proof of the following. If H[les ]G with [G[ratio ]H]∈[ ]*, and if the restriction V[mid ]H is a permutation module (for example, if V is a projective [ ]G-module and H∈Sylp(G)), then β(V, G)[les ]max{[mid ]G[mid ], d([mid ]G[mid ]−1)} regardless of char [ ].