Abstract:

This thesis discusses some problems relating the properties of a set A and those of A+A, when A is a subset of an abelian group. Given a finite abelian group G and A is a subset of G, it is said that A is sumfree if the sets 2A and A are disjoint. Chapter 2 discusses the problem of finding the structure of all large sumfree subsets of G. The complete structure of all largest sumfree subsets of G, are obtained provided all the divisors of order G are congruent to 1 modulo 3. Also partial results are obtained regarding structure of all large maximal sumfree subsets of G. A sumfree set A is maximal if it is not a proper subset of any sumfree set. If there is a divisor of order of G which is not congruent to 1 modulo 3 then structure of all largest sumfree subsets of G was known before. The results in this thesis are based on a recent result of Ben Green and Imre Ruzsa. Chapter 3 improves the 'error term' in asymptotic formula of sigma (G) obtained by Ben Green and Imre Ruzsa, using slight refinement of the methods. Chapter 4 discusses a problem on an additive representation function, using an additive lemma proven by means of graph theory. 