Abstract

Suppose that G is a finite group and that F is a field of characteristic p)0 which is a splitting field for all subgroups of G. Let e0 be the sum of the block idempotents of defect zero in FG, and let V be the set of solutions to g ps1 in G. We show that e0sVq. 2, when p is odd, and e0sVq. 3, when ps2. In the latter case Vq. 2sRq, where R is the set of real elements of 2-defect zero. So e0sVqRqsRq. 2. We also show that e0sVqVq4sVq4 . 2, when ps2, where V4 is the set of solutions to g 4s1. These results give us various criteria for the existence of p-blocks of defect zero.