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Blocks of Defect Zero and Products of Elements of Orderp

✍ Scribed by John C Murray

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 107 KB
Volume: 214
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.1998.7715

No coin nor oath required. For personal study only.

✦ Synopsis

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 e be the sum of the block 0 idempotents of defect zero in FG, and let ⍀ be the set of solutions to g p s 1 in Ž q . 2 Ž q . 3 G. We show that e s ⍀ , when p is odd, and e s ⍀ , when p s 2. In the 0 0 Ž q . 2 q latter case ⍀ s R , where R is the set of real elements of 2-defect zero. So

. We also show that e s ⍀ ⍀ s ⍀ , when p s 2, where 0 0 4 4

⍀ is the set of solutions to g 4 s 1. These results give us various criteria for the 4 existence of p-blocks of defect zero.

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