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 available from this repository)

The full text of this publication is not available from this repository. (Contact us about this Publication)
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: http://kar.kent.ac.uk/id/eprint/515 (The current URI for this page, for reference purposes)
  • Depositors only (login required):