New progress on the multiplier conjecture (Q1918202)

Let \(D\) be an abelian \((v, k, \lambda)\)-difference set. The multiplier conjecture (see, for example, \textit{K. T. Arasu} and \textit{D. Stewart} [Certain implications of the multiplier conjecture, J. Comb. Math. Comb. Comput. 3, 207-211 (1988; Zbl 0725.05022)]) states that every prime \(p\) dividing \(n= k- \lambda\) is a multiplier for \(D\) (i.e. \(Dp= D+ g\) for some element \(g\) of \(G\)). The author has already written several papers on this subject, for example, The multiplier conjecture for elementary abelian groups, J. Comb. Des. 2, No. 3, 117-129 (1994; Zbl 0833.05011), The multiplier conjecture for \(n/n_1= 4\), ibid. 6, 393-397 (1995), and A method of studying the multiplier conjecture and some partial solutions for it, Ars Comb. 39, 5-23 (1995; Zbl 0840.05011). In this paper, he gives a survey of results on the conjecture.