Trace and defect of a block idempotent
type: Item
instance of: scholarly article
title: Trace and defect of a block idempotent
zbMATH Open document ID: 0699.20008
DOI: 10.1016/0021-8693(90)90190-Y
published in: Journal of Algebra
publication date: 1990-01-01T00:00:00Z
review text: The author gives a new proof of R. Brauer's result that the p-part of the dimension of a block algebra B in prime characteristic p is \(p^{2a-d}\) where \(p^ a\) is the p-part of the order of G and d is the defect of B. The proof is based on the known structure of blocks with normal defect groups and the Green correspondence. An application shows that 1 appears in the support of the block idempotent of B if and only if B has maximal defect.
Mathematics Subject Classification ID: 20C20
Mathematics Subject Classification ID: 16S34
Mathematics Subject Classification ID: 20C05
Mathematics Subject Classification ID: 16U99
zbMATH DE Number: 4146232
zbMATH Keywords: dimension
zbMATH Keywords: block algebra
zbMATH Keywords: defect
zbMATH Keywords: normal defect groups
zbMATH Keywords: Green correspondence
zbMATH Keywords: block idempotent
author: Gerhard O. Michler
reviewed by: Burkhard Külshammer
MaRDI profile type: Publication
cites work: Notes on Representations of Finite Groups, I
cites work: Q3804894
cites work: Q3955560
cites work: Q4103728
cites work: On p-blocks of p-solvable groups
cites work: Q3035669
cites work: Q4198893
full work available at URL: 0021-8693(90)90190-y
OpenAlex ID: W2089702366
description: scientific article; zbMATH DE number 4146232