Murray, John C.
Blocks of Defect Zero and Products of
Elements of Order p.
Journal of Algebra, 214 (2).
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.
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