ON SUBSETS OF PARTIAL DIFFERENCE SETS

Let G be a finite group of order v. A k-element subset D of G is called a (v, k, lambda, mu)-partial difference set in G if the expressions gh(-1), for g and h in D with g not equivalent to h, represent each nonidentity element contained in D exactly lambda times and represent each nonidentity element not contained in D exactly mu times. Suppose G is abelian and H is a subgroup of G such that gcd (\H\, \G\/\H\)=1 and \G\/\H\ is odd. In this paper, we show that if D is a partial difference set in G with (d(-1)\d is an element of D) = D, then D boolean AND H is a partial difference set in H.