Long unsplittable zero-sum sequences over a finite cyclic group.

Let be an additively written finite cyclic group of order and let be a minimal zero-sum sequence with elements of , i.e. the sum of elements of is zero, but no proper nontrivial subsequence of has sum zero. is called unsplittable if there do not exist an element in and two elements in such that and the new sequence is still a minimal zero-sum sequence. In this paper, we investigate long unsplittable minimal zero-sum sequences over . Our main result characterizes the structures of all such sequences and shows that the index of is at most 2, provided that the length of is greater than or equal to where is a positive integer with least prime divisor greater than . [ABSTRACT FROM AUTHOR]