SOME CONTRIBUTIONS TO CYCLOTOMIC DIFFERENCE SETS AND ABELIAN DIFFERENCE SETS

The modern theory of sets has been originated by the German Mathematician George Cantor. He published so many papers showing various properties of abstract sets. George Cantor’s work was well received by a famous Mathematician Richard Dedekind and another German Mathematician Gottlob Frege presented the set theory as principles of logic. It was the famous English philosopher Bertrand Russel showed in with the intention of the continuation of a set of all sets lead to a inconsistency and is known as Russell’s paradox. Later on many paradoxes were introduced by several mathematicians as well as logicians. several existence and non-existence results on abelian difference sets were, found in research papers of Arasu, Pott , Jungnicked and Schuildt, and Davis and Jedwab. Difference sets play a extremely significant function in combinational design theory and in communicational engineering. Hall Introduction of the useful concept of multipliers and can be used to investigate the existence question. Also difference sets in subjective cluster were formally introduced by Bruck and a new types of sets were developed known as cyclotomic difference sets, twin prime power difference sets and also spence difference sets