Computing modular invariants of p-groups

Shank, R. James and Wehlau, David L. (2002) Computing modular invariants of p-groups. Journal of Symbolic Computation, 34 (5). pp. 307-327. ISSN 0747-7171. (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided)

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Official URL
http://dx.doi.org/10.1006/jsco.2002.0558

Abstract

Let V be a finite dimensional representation of a p-group, G, over a field, k, of characteristic p. We show that there exists a choice of basis and monomial order for which the ring of invariants, k[V](G), has a finite SAGBI basis. We describe two algorithms for constructing a generating set fork[V]G. We use these methods to analyse k[2V(3)](U3) where U-3 is the p-Sylow subgroup of GL(3)(F-p) and 2V(3) is the sum of two copies of the canonical representation. We give a generating set for k[2V(3)](U3) for p = 3 and prove that the invariants fail to be Cohen-Macaulay for p > 2. We also give a minimal generating set for k[mV(2)](Z/p) were V-2 is the two-dimensional indecomposable representation of the cyclic group Z/p. (C) 2002 Elsevier Science Ltd.. All rights reserved.

Item Type: Article
Uncontrolled keywords: POLYNOMIAL INVARIANTS; SAGBI BASES; RINGS
Subjects: Q Science > QA Mathematics (inc Computing science)
Divisions: Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science
Depositing User: Judith Broom
Date Deposited: 19 Dec 2007 18:18
Last Modified: 30 May 2014 09:46
Resource URI: https://kar.kent.ac.uk/id/eprint/515 (The current URI for this page, for reference purposes)
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