No abstract

The Noether number of a representation is the largest degree of an element in a minimal homogeneous generating set for the corresponding ring of invariants. We compute the Noether number for an arbitrary representation of a cyclic group of prime order, and as a consequence prove the "2p − 3 conjecture."

We consider the ring of coinvariants for modular representations of cyclic groups of prime order. For all cases for which explicit generators for the ring of invariants are known, we give a reduced Gröbner basis for the Hilbert ideal and the corresponding monomial basis for the coinvariants. We also describe the decomposition of the coinvariants as a module over the group ring. For one family of representations, we are able to describe the coinvariants despite the fact that an explicit generating set for the invariants is not known. In all cases our results confirm the conjecture of Harm Derksen and Gregor Kemper on degree bounds for generators of the Hilbert ideal. As an incidental result, we identify the coefficients of the monomials appearing in the orbit product of a terminal variable for the three-dimensional indecomposable representation.

Cataloged from PDF version of article.We consider a finite dimensional modular representation V of a cyclic group of prime order p. We show that two points in V that are in different orbits can be separated by a homogeneous invariant polynomial that has degree one or p and that involves variables from at most two summands in the dual representation. Simultaneously, we describe an explicit construction for a separating set consisting of polynomials with these properties. (C) 2009 Elsevier Inc. All rights reserved

We consider the invariant ring for an indecomposable representation of a cyclic group of order p 2 over a field F of characteristic p. We describe a set of F-algebra generators of this ring of invariants, and thus derive an upper bound for the largest degree of an element in a minimal generating set for the ring of invariants. This bound, as a polynomial in p, is of degree two.