Products of k atoms in Krull monoids

Let H be a Krull monoid with finite class group G such that every class contains a prime divisor. For , let denote the set of all with the following property: There exist atoms such that . It is well-known that the sets are finite intervals whose maxima depend only on G. If , then for every . Suppose that . An elementary counting argument shows that and where is the Davenport constant. In [11] it was proved that for cyclic groups we have for every . In the present paper we show that (under a reasonable condition on the Davenport constant) for every noncyclic group there exists a such that for every . This confirms a conjecture of A. Geroldinger, D. Grynkiewicz, and P. Yuan in [13].