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Inverse zero-sum problems II
Let be an additive finite abelian group. A sequence over 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 is the maximum of
the lengths of the minimal zero-sum sequences over . 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 , 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.Comment: new version contains results related to Davenport's constant only;
other results will be described separatel
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