Cross number invariants of finite abelian groups

We study the conjectured values of the maximal cross number k(G)k(G) of a zero-sum free sequence over a finite abelian group G  , defined by Krause, and the maximal cross number K1(G)K1(G) of a unique factorization sequence over G  , defined by Gao and Wang. We prove that the conjectured values of kk and K1K1 must hold for G⊕CpαG⊕Cpα when they hold for G, given that p   is small compared to the prime factors of exp(G)exp(G). When the prime factors of n are far apart and q   is the largest among them, we prove the conjectured value of K1(G)K1(G) for groups G=Cn⊕CqG=Cn⊕Cq and that of k(G)k(G) for groups G=Cn⊕HqG=Cn⊕Hq, where HqHq is an arbitrary finite abelian q-group.