Long Minimal Zero - Sum Sequences in the Group C

A sequence in an additively written abelian group is called a minimal zero-sum sequence if its sum is the zero element of the group and none of its proper subsequences has sum zero. The structure of the longest minimal zero-sum sequences in the group C2 ⊕C2k is known. Their length is equal to 2k + 1. We characterize the minimal zero-sum sequences in C2 ⊕ C2k (k ≥ 3) with lengths at least 2�k/2�+ 4. In particular the characterization theorem covers sequences whose lengths are just a bit greater than half of the maximum possible one. The characterization cannot be extended in the same form to shorter sequences. The argument is based on structural results about minimal zero-sum sequences in cyclic groups.