Murray, John
(1999)
Blocks of Defect Zero and Products of
Elements of Order p.
Journal of Algebra, 214 (2).
pp. 385399.
ISSN 00218693
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 2defect 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 pblocks of defect zero.
Item Type: 
Article

Keywords: 
Defect Zero; Products of
Elements; Order p; 
Academic Unit: 
Faculty of Science and Engineering > Mathematics and Statistics 
Item ID: 
2037 
Depositing User: 
Dr. John Murray

Date Deposited: 
06 Jul 2010 14:53 
Journal or Publication Title: 
Journal of Algebra 
Publisher: 
Elsevier 
Refereed: 
No 
URI: 

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