Difference Sets with n = 2p^m

Let D be a (v, k, λ) difference set over an abelian group G with even n = k - λ. Assume that t ∈ N satisfies the congruences t = q^fi_i (mod exp(G)) for each prime divisor q_i of n/2 and some integer f_i. In [4] it was shown that t is a multiplier of D provided that n > λ, (n/2, λ) = 1 and (n/2, v) = 1. In this paper we show that the condition n > λ may be removed. As a corollary we obtain that in the case of n = 2p^a when p is a prime, p should be a multiplier of D. This answers an open question mentioned in [2].