The study of sum-free subsets probably originated with a result of Schr, who showed that the set of natural numbers can not be partitioned into finitely many sum-free subsets. Using this he showed that for any positive integer , the Fermat equation has a nontrivial solution for all sufficiently large prime . In this talk we shall see a proof, (which is rather short and not difficult) of this curious fact.
We study the question of obtaining a classification of sum-free subsets in certain special groups called type III groups and counting sum-free subsets in these groups. Our results are build upon and improve the results obtained by Ben Green and Imre Ruzsa.