A new result on difference sets with -1 as multiplier (Q1088990)

Let G be an abelian group of order v and let D be a (v,k,\(\lambda)\)- difference set in G admitting -1 as a multiplier. The following result is well-known: If \(p^ a\) divides \(n=k-\lambda\) (p a prime), then \(p^{a+1}\) divides v [the reviewer, ''Difference sets with multiplier - 1'', Arch. Math. 38, 511-513 (1982; Zbl 0478.05017)]. The author proves the following interesting converse of this result: If an odd prime p divides v, then p divides n. The proof involves rather long character computations. In the meantime, a much shorter proof (only requiring a few computations in the group algebra GF(p)G was given by \textit{A. Pott} in his manuscript ''On abelian difference sets with multiplier -1'' (submitted to Geom. Dedicata).