Contributions to zero-sum problems

A prototype of zero–sum theorems, the well–known theorem of Erdős, Ginzburg and Ziv says that for any positive integer n, any sequence a1, a2, · · · , a2n−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), generated a lot of research and still have challenging open questions. Here we propose a new generalization of the Erdős–Ginzburg–Ziv Theorem and prove it in some basic cases.