On generators of the Hilbert ideal for cyclic groups in modular invariant theory

Let G be a cyclic group of order p(2) and V be a faithful indecomposable representation of G over a field F of characteristic p. We show that the Hilbert ideal of the invariant ring is generated by polynomials of degree at most |G| whenever dim V <= 4p or dim V >= p(2) - 2p, proving a conjecture of Derksen and Kemper in this particular case. (C) 2014 Elsevier Inc. All rights reserved.