Campbell, H.E.A. and GeramitaI., A.V. and Hughes, I.P. and Wehlau, D.L. and Shank, R.J.
Non-Cohen-Macaulay Vector Invariants and a Noether Bound for a Gorenstein Ring of Invariants.
Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques, 42
(Full text available)
This paper contains two essentially independent results in the invariant theory of finite groups. First
we prove that, for any faithful representation of a non-trivial p-group over a field of characteristic p, the ring
of vector invariants ofmcopies of that representation is not Cohen-Macaulay form 3. In the second section
of the paper we use Poincar´e series methods to produce upper bounds for the degrees of the generators for
the ring of invariants as long as that ring is Gorenstein. We prove that, for a finite non-trivial group G and
a faithful representation of dimension n with n > 1, if the ring of invariants is Gorenstein then the ring is
generated in degrees less than or equal to n(jGj − 1). If the ring of invariants is a hypersurface, the upper
bound can be improved to [G].
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