PERFECT SUMSETS IN FINITE ABELIAN-GROUPS

We prove that if G is a finite abelian group of odd order n and A subs et of G is of size a such that for every g is an element of G there ex ist u, v is an element of A with g = u + v, then n less than or equal to [(a - 1)(2) + 1]/2 if a is even and n less than or equal to [(a - 1 )(2) + 2]/2 if a is odd. We show that equality occurs if and only if n is an element of {3, 5, 9, 13, 25, 243}.