The Noether Map II
Mara D Neusel and M"ufit Sezer

Abstract:
Let $\rho: G\hookrightarrow GL(n, F)$ be a faithful representation of a finite group G.
In this paper we proceed with the study of the image of the associated Noether map 
\[
\eta_G^G: F[V(G)]^G \longrightarrow F[V]^G.
\]
In [Noether Map I] it has been shown that the Noether map is surjective if $V$ is a
projective $FG$-module. This paper deals with the converse. The converse
is in general not true: we illustrate this with an example. However, for $p$-groups 
(where $p$ is the characteristic of the ground field $F$) as well as for 
permutation representations of any group the surjectivity of the Noether map implies 
the projectivity of $V$.