Brauer's height zero conjecture for central quotients of special linear and special unitary groups
type: Item
instance of: scholarly article
title: Brauer's height zero conjecture for central quotients of special linear and special unitary groups
zbMATH Open document ID: 0930.20008
author: Harvey I. Blau
author: Harald Ellers
published in: Journal of Algebra
publication date: 1999-11-23T00:00:00Z
review text: Let \(G\) be a finite group and \(B\) be any \(r\)-block of \(G\), where \(r\) is a prime number. By the height of an irreducible character \(\chi\) belonging to \(B\) we mean \(\nu(\chi(1))-\nu([G:D])\) where \(D\) is a defect group of \(B\) and \(\nu\) is the discrete valuation associated to \(r\). Brauer's height zero conjecture states that all ordinary irreducible characters of \(G\) belonging to any \(r\)-block \(B\) have height zero if and only if \(B\) has an Abelian defect group. This conjecture has been verified by \textit{P. Fong} and \textit{B. Srinivasan} [Invent. Math. 69, 109-153 (1982; Zbl 0507.20007)] for all \(r\)-blocks of all the general linear and unitary groups over finite fields where \(r>2\) and is different from the characteristic of the ground field. The purpose of the paper under review is to prove Brauer's height zero conjecture for all \(r\)-blocks of all central factor groups of the special linear and special unitary groups.
Mathematics Subject Classification ID: 20C20
Mathematics Subject Classification ID: 20G05
Mathematics Subject Classification ID: 20G40
zbMATH DE Number: 1271822
zbMATH Keywords: special linear groups
zbMATH Keywords: blocks
zbMATH Keywords: finite groups
zbMATH Keywords: Brauer's height zero conjecture
zbMATH Keywords: irreducible characters
zbMATH Keywords: Abelian defect groups
zbMATH Keywords: unitary groups
reviewed by: M. R. Darafsheh
Wikidata QID: Q122928526
MaRDI profile type: Publication
full work available at URL: jabr.1998.7661
OpenAlex ID: W2076240892
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DOI: 10.1006/JABR.1998.7661
description: scientific article; zbMATH DE number 1271822