The Cross Number of Zero-sum Free Sequences in Finite Abelian Groups

Bumsoo Kim

Published 2014-10-25Version 1

We study the maximal cross number $\mathsf{k}(G)$ of a zero-sum free sequence over a finite abelian group $G$, defined by Krause and Zahlten. In the first part of this paper, we extend a previous result by X. He to prove that the value of $\mathsf{k}(G)$ conjectured by Krause and Zahlten hold for $G \bigoplus C_{p^a} \bigoplus C_{p^b}$ when it holds for $G$. In the second part, we describe a new method for proving that the conjectured value of $\mathsf{k}(G)$ hold for abelian groups of the form $H_p \bigoplus C_{q^m}$ (where $H_p$ is any finite abelian $p$-group) and $C_p \bigoplus C_q \bigoplus C_r$ without restrictions on the primes $p,q,r$.