Multiplier theorems

We state and prove a multiplier theorem for a central element A of ZG, the group ring over Z of a group G. This generalizes most previously known multiplier theorems for difference sets and divisible difference sets. We also provide applications to show that our theorem provides new multipliers and establish the nonexistence of a family of divisible difference sets which correspond to elliptic semiplanes admitting a regular collineation group. © 1995 John Wiley & Sons, Inc.