Brauer's \(k(B)\)-conjecture for solvable \(3'\)-groups
type: Item
instance of: scholarly article
title: Brauer's \(k(B)\)-conjecture for solvable \(3'\)-groups
zbMATH Open document ID: 0807.20013
author: Alberto Espuelas
published in: Journal of Algebra
publication date: 1995-01-16T00:00:00Z
review text: R. Brauer asked whether the number of ordinary irreducible characters in a \(p\)-block of a finite group is bounded by the order of its defect group. In the case of \(p\)-solvable groups it suffices to prove a statement about the number of characters in certain group extensions. Here very significant contributions have been given by R. Knörr. The author proves: Main theorem. Let \(G\) be a solvable \(3'\)-group and let \(V\) be a faithful \(KG\)-module, where \(\text{char}(K) \neq 3\) and \(\text{char}(K) \nmid | G|\). Then there exists \(v \in V\) such that \(V_{C_ G(v)}\) is a permutation module. By a recent result Knörr this verifies the conjecture for solvable \(3'\)-groups.
Mathematics Subject Classification ID: 20C20
Mathematics Subject Classification ID: 20D10
Mathematics Subject Classification ID: 20C05
Mathematics Subject Classification ID: 20D60
zbMATH DE Number: 579544
zbMATH Keywords: irreducible characters
zbMATH Keywords: \(p\)-blocks
zbMATH Keywords: finite groups
zbMATH Keywords: order
zbMATH Keywords: defect groups
zbMATH Keywords: \(p\)-solvable groups
zbMATH Keywords: number of characters
zbMATH Keywords: permutation modules
zbMATH Keywords: solvable \(3'\)-groups
MaRDI profile type: Publication
full work available at URL: jabr.1994.1084
OpenAlex ID: W1978683241
Wikidata QID: Q123007686
DOI: 10.1006/JABR.1994.1084
description: scientific article; zbMATH DE number 579544