A combinatorial problem on finite Abelian groups

In this paper the Following theorem is proved. Let G be a finite Abelian group of order ii. Then, n + D(G)-1 is the least integer rn with the properly that for any sequence of m elements a(1), ..., a(m) in G, 0 can he written in the form 0 = a(1)+...+ a(in) with 1 less than or equal to i(1) <...< i(n) less than or equal to m, where D(G) is the Davenport's constant on G, i.e., the least integer n with the property that for any sequence of d elements in G, there exists a nonempty subsequence that the sum of whose elements is 0. (C) 1996 Academic Press, Inc.