On degree bounds for invariant rings of finite groups over
finite fields.

Peter Fleischmann and Wolfgang Lempken
Institute for Experimental Mathematics
University of Essen
Ellernstr. 29, 45326 Essen, Germany
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In this paper we give an outline on known results 
(with some new proofs) on degree bounds for invariant
algebras over arbitrary commutative 
rings and arbitary finite groups. 
We also present some new results on the range of finite fields 
over which Noether's degree bound holds for subgroups
of classical groups. We also prove that it holds in the
`coprime case' for groups with only cyclic or alternating
composition factors.