Dade's projective conjecture for \(p\)-solvable groups
type: Item
instance of: scholarly article
title: Dade's projective conjecture for \(p\)-solvable groups
zbMATH Open document ID: 0955.20006
author: Geoffrey R. Robinson
published in: Journal of Algebra
publication date: 2001-02-27T00:00:00Z
review text: Dade's conjecture relates the number of irreducible characters of fixed defect in a \(p\)-block \(B\) of a finite group \(G\) to similar numbers in Brauer correspondents of \(B\) in \(p\)-local subgroups of \(G\). In the paper under review, the author proves the projective form of this conjecture for the class of \(p\)-solvable groups. More generally, he shows that in a minimal counterexample (if it exists) to this form of the conjecture every \(p\)-solvable normal subgroup is central. (Dade himself had indicated the possibility that his conjectures ultimately reduce to simple groups.)
reviewed by: Burkhard Külshammer
Mathematics Subject Classification ID: 20C20
Mathematics Subject Classification ID: 20C05
Mathematics Subject Classification ID: 20D10
zbMATH DE Number: 1496011
zbMATH Keywords: subpairs
zbMATH Keywords: Brauer correspondence
zbMATH Keywords: Fong correspondence
zbMATH Keywords: Dade conjecture
zbMATH Keywords: numbers of irreducible characters
zbMATH Keywords: defect groups
zbMATH Keywords: \(p\)-blocks
zbMATH Keywords: \(p\)-local subgroups
zbMATH Keywords: \(p\)-solvable groups
Wikidata QID: Q123224052
MaRDI profile type: Publication
full work available at URL: jabr.2000.8307
OpenAlex ID: W1997311462
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DOI: 10.1006/JABR.2000.8307
description: scientific article; zbMATH DE number 1496011