Zero-sum problems and coverings by proper cosets

Let G be a finite Abelian group and D(G) its Davenport constant, which is defined as the maximal length of a minimal zero-sum sequence in G. We show that various problems on zero-sum sequences in G may be interpreted as certain covering problems. Using this approach we study the Davenport constant of groups of the form (Z/nZ)r, with n≥2 and r∈N. For elementary p-groups G, we derive a result on the structure of minimal zero-sum sequences S having maximal length |S|=D(G).