Perfect sumsets in finite Abelian groups

AbstractWe prove that if G is a finite abelian group of odd order n and A ⊂ G is of size a such that for every g ϵ G there exist u, v ϵ A with g = u + v, then n ≤ [(a - 1)2 + 1]2 if a is even and n ≤ [(a - 1)2 + 2]/2 if a is odd. We show that equality occurs if and only if n ϵ {3, 5, 9, 13, 25, 243}