Perfect isometries for blocks with abelian defect groups and Klein four inertial quotients
type: Item
instance of: scholarly article
title: Perfect isometries for blocks with abelian defect groups and Klein four inertial quotients
zbMATH Open document ID: 0789.20009
author: Lluis Puig
author: Yoko Usami
published in: Journal of Algebra
publication date: 1994-01-06T00:00:00Z
review text: Let \(G\) be a finite group, and let \(B\) be a block of \(G\) with abelian defect group \(P\). Moreover, let \(\beta\) be a block of \(C_ G(P)\) such that \(\beta^ G = B\), and suppose that the inertial quotient \(N_ G(P,\beta)/C_ G(P)\) is a Klein four group. In this situation the authors construct a perfect isometry between the group of generalized characters in \(B\) and the group of generalized characters in the Brauer correspondent \(b\) of \(B\) in \(N_ G(P)\). This confirms a conjecture of M. Broué for this case. It follows that \(B\) and \(b\) have the same number of irreducible Brauer characters and that the block algebras of \(B\) and \(b\) have isomorphic centers.
reviewed by: Burkhard Külshammer
Mathematics Subject Classification ID: 20C20
Mathematics Subject Classification ID: 20C05
zbMATH DE Number: 436487
zbMATH Keywords: Alperin conjecture
zbMATH Keywords: finite group
zbMATH Keywords: block
zbMATH Keywords: abelian defect group
zbMATH Keywords: perfect isometry
zbMATH Keywords: generalized characters
zbMATH Keywords: Brauer correspondent
zbMATH Keywords: irreducible Brauer characters
zbMATH Keywords: block algebras
MaRDI profile type: Publication
full work available at URL: jabr.1993.1184
OpenAlex ID: W2000829604
DOI: 10.1006/JABR.1993.1184
description: scientific article; zbMATH DE number 436487