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

Let G be a cyclic group of order p2 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≥p2−2p, proving a conjecture of Derksen and Kemper in this particular case.