On Brauer's \(k(B)\)-problem for blocks with metacyclic defect groups of odd order.
type: Item
instance of: scholarly article
title: On Brauer's \(k(B)\)-problem for blocks with metacyclic defect groups of odd order.
zbMATH Open document ID: 1233.20011
author: Sheng Gao
published in: Archiv der Mathematik
publication date: 2011-10-11T00:00:00Z
review text: A famous conjecture in the modular representation theory of finite groups is Brauer's \(k(B)\)-problem which states that if \(G\) is a finite group, \(p\) a prime and \(B\) a \(p\)-block of \(G\) with defect group \(D\), then the number \(k(B)\) of ordinary irreducible characters in \(B\) is bounded above by \(|D|\). In the paper under review, the conjecture is proved under the additional hypothesis that \(D\) is metacyclic and \(p\) is odd.
reviewed by: Thomas Michael Keller
Mathematics Subject Classification ID: 20C20
Mathematics Subject Classification ID: 20C15
zbMATH DE Number: 5956235
zbMATH Keywords: characters
zbMATH Keywords: blocks
zbMATH Keywords: defect groups
zbMATH Keywords: metacyclic groups
zbMATH Keywords: Brauer \(k(B)\)-conjecture
zbMATH Keywords: numbers of irreducible characters
MaRDI profile type: Publication
full work available at URL: s00013-011-0265-y
OpenAlex ID: W2044746795
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DOI: 10.1007/S00013-011-0265-Y
description: scientific article; zbMATH DE number 5956235