An inequality of block invariants
type: Item
instance of: scholarly article
title: An inequality of block invariants
zbMATH Open document ID: 0886.20008
published in: Journal of Algebra
publication date: 1998-05-12T00:00:00Z
review text: Let \(B\) be a block of a finite group \(G\) with normal abelian defect group \(D\). The author proves that \(k(B)+|D|\leq(e_B+1)m_B\) where \(k(B)\) is the number of irreducible ordinary characters in \(B\), \(e_B\) is the inertial index of \(B\) and \(m_B\) is the number of (major) \(B\)-subsections. Moreover, if the inertial factor group of \(B\) is cyclic then \(2m_B\sqrt{e_B}\leq k(B)+|D|\).
Mathematics Subject Classification ID: 20C20
Mathematics Subject Classification ID: 20C05
Mathematics Subject Classification ID: 20D60
zbMATH DE Number: 1051585
zbMATH Keywords: subsections
zbMATH Keywords: blocks
zbMATH Keywords: finite groups
zbMATH Keywords: Abelian defect groups
zbMATH Keywords: numbers of irreducible ordinary characters
zbMATH Keywords: inertial index
author: Jiwen Zeng
reviewed by: Burkhard Külshammer
MaRDI profile type: Publication
full work available at URL: jabr.1996.7009
OpenAlex ID: W2001215431
cites work: Q3804896
cites work: Brauer coefficients of p-subgroups associated with a p-block of a finite group
cites work: Lower defect groups
cites work: Q3934589
cites work: On Brauer's \(k(B)\) problem
DOI: 10.1006/JABR.1996.7009
description: scientific article; zbMATH DE number 1051585