# Non-Cohen-Macaulay Vector Invariants and a Noether Bound for a Gorenstein Ring of Invariants

Campbell, Eddy, GeramitaI, A.V., Hughes, I.P., Wehlau, David L., Shank, R. James (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. (KAR id:4643)

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## 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].

Item Type: Article Q Science > QA Mathematics (inc Computing science) > QA150 Algebra Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science James Shank 13 Jun 2009 13:24 UTC 16 Nov 2021 09:42 UTC https://kar.kent.ac.uk/id/eprint/4643 (The current URI for this page, for reference purposes) https://orcid.org/0000-0002-3317-4088