The strengthened Alperin weight conjecture for \(p\)-solvable groups.
type: Item
instance of: scholarly article
title: The strengthened Alperin weight conjecture for \(p\)-solvable groups.
zbMATH Open document ID: 1342.20010
author: Alexandre Turull
published in: Journal of Algebra
publication date: 2014-08-27T00:00:00Z
reviewed by: Thomas Michael Keller
Mathematics Subject Classification ID: 20C20
Mathematics Subject Classification ID: 20C15
zbMATH DE Number: 6334764
zbMATH Keywords: Clifford theory
zbMATH Keywords: representations of finite groups
zbMATH Keywords: Alperin weight conjecture
zbMATH Keywords: character correspondences
zbMATH Keywords: irreducible \(p\)-Brauer characters
MaRDI profile type: Publication
Wikidata QID: Q123166147
full work available at URL: j.jalgebra.2013.02.006
OpenAlex ID: W2066160194
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DOI: 10.1016/J.JALGEBRA.2013.02.006
review text: The well-known Alperin Weight Conjecture is an important conjecture in the area of representation theory of finite groups. We refer to the paper for a succinct description of the conjecture and related conjectures, and for what is known about it. For this review it should suffice to say that for a finite group \(G\) and a prime \(p\) the conjecture claims the existence of a bijection between the irreducible \(p\)-Brauer characters of \(G\) and the conjugacy classes of \(p\)-weights of \(G\). A recent strategy to approach this and related conjectures has been to impose various extra conditions on the bijection and thereby strengthening the conjecture in the hope that, besides of getting more information, a general proof might become easier.NEWLINENEWLINE In the paper under review the author proves a very strong form of the conjecture for \(p\)-solvable groups. This, in particular, proves, for \(p\)-solvable groups, a strengthening that had been proposed by \textit{G. Navarro} [Ann. Math. (2) 160, No. 3, 1129-1140 (2005; Zbl 1079.20010)].
description: scientific article; zbMATH DE number 6334764