Skip to main content

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)

PDF Publisher pdf
Language: English
Click to download this file (83kB) Preview
[thumbnail of campbell7304.pdf]
This file may not be suitable for users of assistive technology.
Request an accessible format


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
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: (The current URI for this page, for reference purposes)
Shank, R. James:
  • Depositors only (login required):

Total unique views for this document in KAR since July 2020. For more details click on the image.