Local control in fusion systems of \(p\)-blocks of finite groups.
type: Item
instance of: scholarly article
title: Local control in fusion systems of \(p\)-blocks of finite groups.
zbMATH Open document ID: 1053.20007
DOI: 10.1016/S0021-8693(02)00517-3
author: Radha Kessar
author: Markus Linckelmann
author: Geoffrey R. Robinson
published in: Journal of Algebra
publication date: 2003-02-12T00:00:00Z
review text: The authors prove a block theoretic analogue of Glauberman's \(ZJ\)-theorem: If \(p\) is an odd prime, \(b\) a \(p\)-block of a finite group \(G\) such that \(\text{SL}(2,p)\) is not involved in \(N_G(Q,e)/C_G(Q)\) for any \(b\)-subpair \((Q,e)\), then \(N_G(Z(J(P)))\) controls \(b\)-fusion, where \(P\) is a defect group of \(b\) and \(J(P)\) denotes the Thompson subgroup of \(P\). Several results of general interest about fusion and blocks are also included in the paper.
Mathematics Subject Classification ID: 20C20
Mathematics Subject Classification ID: 20D20
Mathematics Subject Classification ID: 16P10
Mathematics Subject Classification ID: 16L60
zbMATH DE Number: 1868069
zbMATH Keywords: Glauberman functors
zbMATH Keywords: defect groups
zbMATH Keywords: Brauer categories
zbMATH Keywords: Alperin-Goldschmidt conjugation
MaRDI profile type: Publication
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full work available at URL: s0021-8693(02)00517-3
OpenAlex ID: W2064096425
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description: scientific article; zbMATH DE number 1868069