On non-Abelian group difference sets

This paper is motivated by R. H. Bruck’s paper[3], in which he proved that the existence of cyclic projective plane of order n ≡ 1 (mod 3) implies that of a non-planar difference set of the same order by proving that such a cyclic projective plane admits a regular non-Abelian automorphism group using n as a multiplier. In this paper we will discuss in detail the possibility of using multipliers to construct more non-Abelian difference sets from known difference sets, especially from cyclic ones. The existence of several infinite families of non-Abelian group different sets will be established.