Perfect isometries for blocks with abelian defect groups and dihedral inertial quotients of order \(6\)
type: Item
instance of: scholarly article
title: Perfect isometries for blocks with abelian defect groups and dihedral inertial quotients of order \(6\)
zbMATH Open document ID: 0831.20011
author: Yoko Usami
published in: Journal of Algebra
publication date: 1996-02-08T00:00:00Z
review text: Let \(b\) be a block of a finite group \(G\) with abelian defect group \(P\). A conjecture by M. Broué says that \(b\) is isotypic to its Brauer correspondent \(c\) in \(N_G(P)\). The author verifies this conjecture in the special case where the inertial quotient \(N_G(P, e)/PC_G(P)\) is dihedral of order 6; here \(e\) denotes a block of \(C_G(P)\) such that \(e^G = b\). In previous papers, some of them joint with L. Puig, the author had proved a similar result for the case \(|N_G(P,e)/PC_G(P) |\leq 4\).
Mathematics Subject Classification ID: 20C20
Mathematics Subject Classification ID: 20C05
Mathematics Subject Classification ID: 16S34
zbMATH DE Number: 763909
zbMATH Keywords: perfect isometry
zbMATH Keywords: isotypy
zbMATH Keywords: Brauer's height zero conjecture
zbMATH Keywords: Alperin's weight conjecture
zbMATH Keywords: block with abelian defect group
zbMATH Keywords: finite groups
zbMATH Keywords: Brauer correspondent
zbMATH Keywords: inertial quotient
reviewed by: Burkhard Külshammer
MaRDI profile type: Publication
full work available at URL: jabr.1995.1051
OpenAlex ID: W1990058966
DOI: 10.1006/JABR.1995.1051
description: scientific article; zbMATH DE number 763909