The module structure of a group action on a polynomial ring: A finiteness theorem

Authors:
Dikran B. Karagueuzian and Peter Symonds

Journal:
J. Amer. Math. Soc. **20** (2007), 931-967

MSC (2000):
Primary 16W22; Secondary 20C20

DOI:
https://doi.org/10.1090/S0894-0347-07-00563-2

Published electronically:
April 11, 2007

MathSciNet review:
2328711

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Consider a group acting on a polynomial ring over a finite field. We study the polynomial ring as a module for the group and prove a structure theorem with several striking corollaries. For example, any indecomposable module that appears as a summand must also appear in low degree, and so the number of isomorphism types of such summands is finite. There are also applications to invariant theory, giving a priori bounds on the degrees of the generators.

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Additional Information

**Dikran B. Karagueuzian**

Affiliation:
Mathematics Department, Binghamton University, P.O. Box 6000, Binghamton, New York 13902-6000

Email:
dikran@math.binghamton.edu

**Peter Symonds**

Affiliation:
School of Mathematics, University of Manchester, P.O. Box 88, Manchester M60 1QD, United Kingdom

Email:
Peter.Symonds@manchester.ac.uk

Received by editor(s):
March 17, 2005

Published electronically:
April 11, 2007

Article copyright:
© Copyright 2007
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.