An addition theorem for finite Abelian groups

Abstract If g1, g2, …, g2n−1 is a sequence of 2n − 1 elements in an Abelian group G of order n, it is known that there are n distinct indices i1, i2, …, in such that 0 = gi1 + gi2 + ⋯ + gin. In this paper a suitably general condition on the sequence is given which insures that every element g in G has a representation g = gi1 + gi2 + ⋯ + gin as the sum of n terms of the sequence.