The theory of difference sets and relative difference sets has been used to investigate finite projective planes which admit a quasiregular collineation group of “reasonably” large order (see 14, 51.) In this paper we introduce the concept of a direct product difference set (and, in Section 6, a generalized d.p. difference set) to aid our investigation of quasiregular collineation groups. In Section 2 we define a d.p. difference set and show that such a difference set must have parameters of a… CONTINUE READING