MINIMAL ZERO-SUM SEQUENCES IN FINITE CYCLIC GROUPS

Let C-n be the cyclic group of order n, n >= 20, and let S Pi(k)(i=1) gi be a minimal zero-sum sequence of elements in C-n. We say that S is insplitable if for any g(i) is an element of S and any two elements x, y is an element of C-n satisfying x + y = g(i), Sg(i)(-1)xy is not a minimal zero-sum sequence any more. We define Index(S) = min((m,n)=1){Sigma(k)(i=1)vertical bar mg(i)vertical bar}, where vertical bar x vertical bar denotes the least positive inverse image under homomorphism from the additive group of integers Z onto C-n. In this paper we prove that for an insplitable minimal zero-sum sequence S, if Index(S) = 2n, then vertical bar S vertical bar <= left perpendicular n/1 right perpendicular + 1.