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 [ ].