On subsets of partial difference sets

Abstract Let G be a finite group of order v . A k -element subset D of G is called a ( v , k , λ , μ )-partial difference set in G if the expressions gh −1 , for g and h in D with g ≠ h , represent each nonidentity element contained in D exactly λ times and represent each nonidentity element not contained in D exactly μ 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 ∈ D } = D , then D ∩ H is a partial difference set in H .