  In this paper, we study a combinatorial problem originating in the following
conjecture of Erdos and Lemke: given any sequence of n divisors of n,
repetitions being allowed, there exists a subsequence the elements of which are
summing to n. This conjecture was proved by Kleitman and Lemke, who then
extended the original question to a problem on a zero-sum invariant in the
framework of finite Abelian groups. Building among others on earlier works by
Alon and Dubiner and by the author, our main theorem gives a new upper bound
for this invariant in the general case, and provides its right order of
magnitude.

Combinatorics;Group Theory;Number Theory