Alperin-McKay implies Brauer's problem 21
type: Item
instance of: scholarly article
title: Alperin-McKay implies Brauer's problem 21
zbMATH Open document ID: 0846.20013
author: Geoffrey R. Robinson
author: Burkhard Külshammer
published in: Journal of Algebra
publication date: 1996-06-03T00:00:00Z
review text: A connection between two problems in modular representation theory of finite groups is proved, based on Zelmanov's solution of the restricted Burnside problem. R. Brauer's Problem 21 is whether the order of the defect group of a \(p\)-block is bounded in terms of the number of ordinary irreducible characters in the block. The Alperin-McKay conjecture asserts that a \(p\)-block and its Brauer correspondent have the same number of characters of height 0.
Mathematics Subject Classification ID: 20C20
Mathematics Subject Classification ID: 20D60
zbMATH DE Number: 869810
zbMATH Keywords: orders of defect groups
zbMATH Keywords: modular representations
zbMATH Keywords: finite groups
zbMATH Keywords: \(p\)-blocks
zbMATH Keywords: ordinary irreducible characters
zbMATH Keywords: Brauer correspondence
zbMATH Keywords: number of characters
MaRDI profile type: Publication
full work available at URL: jabr.1996.0062
OpenAlex ID: W2029614003
DOI: 10.1006/JABR.1996.0062
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description: scientific article; zbMATH DE number 869810