The Noether Map II
Mara D Neusel and M"ufit Sezer
mara.d.neusel@ttu.edu mufit.sezer@boun.edu.tr
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
$V$.
Note that this paper together with noether-map-I contain stronger results
than the authors' previous paper Neusel-Sezer/noether.