Blocks of Defect Zero and Products of Elements of Orderp

Suppose thatGis a finite group and thatFis a field of characteristicp > 0 which is a splitting field for all subgroups ofG. Lete0be the sum of the block idempotents of defect zero inFG, and let Ω be the set of solutions togp = 1 inG. We show thate0 = (Ω + )2, whenpis odd, ande0 = (Ω + )3, whenp = 2. In the latter case (Ω + )2 = R + , whereRis the set of real elements of 2-defect zero. Soe0 = Ω + R + = (R + )2. We also show thate0 = Ω + Ω + 4 = (Ω + 4)2, whenp = 2, where Ω4is the set of solutions tog4 = 1. These results give us various criteria for the existence ofp-blocks of defect zero.