Contributions to zero-sum problems

A prototype of zero-sum theorems, the well-known theorem of Erdos, Ginzburg and Ziv says that for any positive integer n, any sequence a(1), a(2),..., a(2n-1) of (2n-1) integers has a subsequence of n elements whose sum is 0 modulo n. Appropriate generalizations of the question, especially that for (Z/pZ)(d), generated a lot of research and still have challenging open questions. Here we propose a new generalization of the Erdos-Ginzburg-Ziv theorem and prove it in some basic cases. (c) 2005 Elsevier B.V. All rights reserved.