Let G be a finite abelian group. A subset A of G is called sum free if the equation a+b=c has no solution in A. Ben Green and Rusza recently determined the maximum cardinality of a sum free set. They also characterized the sum free sets with maximum cardinality for groups of Type 1 and 2. In this talk we shall indicate our recent results on the characterization of sum free set with maximum cardinality for groups of type 3. This is a joint work with Dr. Surya Ramana and Dr. Gyan Prakash.