Let G be a finite abelian group of order n. A subset A of G is said to be a zero-sum set if the sum of all its elements is zero. The Olson's constant Ol(G) is defined to be the smallest integer t such that every set of t elements contains a zero-sum subset. Szemeredi proved that Ol(G) < c n^{1/2}, c being an absolute constant and this constant is now known to be 2^{1/2} for cyclic groups.
We will present similar results for Z_p + Z_p which are obtained by using combinatorics and exponential sums.
Gautami Bhowmik