On the size of the multiplier groups of cyclic difference sets

Using a result of Cohen [J. Combin. Theory Ser. A 51 (1989), 227–236], we get an upper bound for the size of the multiplier group of a cyclic difference set; this generalizes a result of Ho [J. Algebra 148 (1992), 325–336] on the multiplier groups of cyclic projective planes to arbitrary λ.