Maximal sum-free sets in finite abelian groups

Abstract

A subset S of an additive group G is called a maximal sum-free set in G if (S+S) ∩ S = ø and ∣S∣ ≥ ∣T∣ for every sum-free set T in G. It is shown that if G is an elementary abelian p–group of order pⁿ, where p = 3k ± 1, then a maximal sum-free set in G has kp^n-1 elements. The maximal sum-free sets in Z_p are characterized to within automorphism.