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The Noether map II

Authors:	Mara D Neusel Mü fit Sezer

Institution:	Department of Mathematics, Texas Tech University, Lubbock, Texas 79409 ; Department of Mathematics and Statistics, Bogazici Üniversitesi, MS 1042, Bebek, Istanbul, Turkey

Abstract:	Let $\rho: G\hookrightarrow \mathrm{GL}(n, \mathbb{F})$ be a faithful representation of a finite group . In this paper we proceed with the study of the image of the associated Noether map $\displaystyle \eta_G^G: \mathbb{F}V(G)]^G \rightarrow\mathbb{F}V]^G.$ In our 2005 paper it has been shown that the Noether map is surjective if is a projective $\mathbb{F} G$ -module. This paper deals with the converse. The converse is in general not true: we illustrate this with an example. However, for -groups (where is the characteristic of the ground field $\mathbb{F}$ ) as well as for permutation representations of any group the surjectivity of the Noether map implies the projectivity of .

Keywords:	Invariant theory of finite groups Noether map modular invariant theory projective $\mathbb{F}G$-modules $p$-groups permutation representations

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