Campbell, H.E.A. and GeramitaI., A.V. and Hughes, I.P. and Wehlau, D.L. and Shank, R.J.
(1999)
Non-Cohen-Macaulay Vector Invariants and a Noether Bound for a Gorenstein Ring of Invariants.
Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques, 42
(2).
pp. 155-161.
ISSN 0008-4395.
Abstract
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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