Campbell, Eddy, GeramitaI, A.V., Hughes, I.P., Wehlau, David L., Shank, R. James (1999) NonCohenMacaulay Vector Invariants and a Noether Bound for a Gorenstein Ring of Invariants. Canadian Mathematical BulletinBulletin Canadien De Mathematiques, 42 (2). pp. 155161. ISSN 00084395. (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 nontrivial pgroup over a field of characteristic p, the ring
of vector invariants ofmcopies of that representation is not CohenMacaulay 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 nontrivial 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 

Subjects:  Q Science > QA Mathematics (inc Computing science) > QA150 Algebra 
Divisions:  Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science 
Depositing User:  James Shank 
Date Deposited:  13 Jun 2009 13:24 UTC 
Last Modified:  16 Nov 2021 09:42 UTC 
Resource URI:  https://kar.kent.ac.uk/id/eprint/4643 (The current URI for this page, for reference purposes) 
Shank, R. James:  https://orcid.org/0000000233174088 
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