For (G,+,0) a finite abelian group and S=g1…gk a sequence over G, we denote by σ(S) the sum of all terms of S. We call |S|=k the length of the sequence. If the sum of S is 0, we say that S is a zero-sum sequence. We denote by B(G) the set of all zero-sum sequences over G. This is a submonoid of the monoid of all sequences over G. We say that a zero-sum sequence is a minimal zero-sum sequence if it cannot be decomposed into two non-empty zero-sum subsequences. In other words, this means that it is an irreducible element in B(G). For S∈B(G) we say that ℓ is a factorization-length of S if there are minimal zero-sum sequences A1,…,Aℓ over G such that S=A1…Al. We denote the set of all ℓ that are a factorization-length of S by L(S).