On generators of modular invariant rings of finite groups

Peter Fleischmann and Wolfgang Lempken
Institute for Experimental Mathematics
University of Essen
Ellernstr. 29, 45326 Essen, Germany
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The paper is to appear in Bull.LMS


Abstract:

In this paper we present a constructive proof of the following: 
Let $G$ act on the polynomial ring $F[V]$ ($V \in F[G]-mod$).
If $H\le G$ 
with index $[G:H]$ invertible in $F$ such that
the restriction $V_{|H}$ is a permutation module (e.g. if $V$ is
a projective $FG$ - module and $H\in Syl_p(G)$) then the degree bound
$\beta(V,G)$ for generators of $F[V]^G$ is less or equal to
$max\{|G|, dim V (|G|-1)\}$.