The author generalizes a lemma of Arasu and Ma and applies this to obtain some necessary existence conditions for difference sets which avoid the strong technical assumption of self-conjugacy. In particular, he verifies Lander's conjecture (saying that the Sylow \(p\)-subgroup of the underlying group \(G\) cannot be cyclic if \(G\) is abelian and \(p\) divides both the group order \(v\) and the order \(n=k-\lambda\) of the difference set) for the McFarland, Spence, Davis-Jedwab and Chen families.