Inverse zero-sum problems II

2008/01/24 by Schmid, Wolfgang A. · 2 citations
#11B50 #11B75 #11P70 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.0801.3747

Abstract

Let G be an additive finite abelian group. A sequence over G is called a minimal zero-sum sequence if the sum of its terms is zero and no proper subsequence has this property. Davenport's constant of G is the maximum of the lengths of the minimal zero-sum sequences over G. Its value is well-known for groups of rank two. We investigate the structure of minimal zero-sum sequences of maximal length for groups of rank two. Assuming a well-supported conjecture on this problem for groups of the form C_m ⊕ C_m, we determine the structure of these sequences for groups of rank two. Combining our result and partial results on this conjecture, yields unconditional results for certain groups of rank two.

Cited by

• The structure of sequences with zero-sum subsequences of the same length on finite abelian groups of rank two
• On separating sets of polynomial invariants of finite abelian group actions

Related

• Inverse Zero-Sum Problems III
• Inverse Zero-Sum Problems III: Addendum
• Restricted inverse zero-sum problems in groups of rank two
• The structure of sequences with zero-sum subsequences of the same length on finite abelian groups of rank two
• On the inverse problem of the k-th Davenport constants for groups of rank 2