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The Noether map II |
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| Authors: | Mara D. Neusel Mü fit Sezer |
| Affiliation: | Department of Mathematics, Texas Tech University, Lubbock, Texas 79409 ; Department of Mathematics and Statistics, Bogazici Üniversitesi, MS 1042, Bebek, Istanbul, Turkey |
| Abstract: | Let  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 rightarrowmathbb{F}[V]^G. $](http://www.ams.org/proc/2007-135-08/S0002-9939-07-08915-0/gif-abstract0/img3.gif){kind=small}  is a projective  -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  ) 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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