Extensions of unipotent characters and the inductive McKay condition.
type: Item
instance of: scholarly article
title: Extensions of unipotent characters and the inductive McKay condition.
zbMATH Open document ID: 1163.20003
author: Gunter Malle
published in: Journal of Algebra
publication date: 2008-12-02T00:00:00Z
review text: One of the main conjectures in the representation theory is the McKay conjecture: for every finite group \(G\) and every prime number \(p\) \[ |\text{Irr}_{p'}(G)|=|\text{Irr}_{p'}(N_G(P))|, \] where \(P\) is a Sylow \(p\)-subgroup of \(G\). The author has shown that the McKay conjecture is true if every finite simple group is good for every prime divisor of its order. In this paper it is proved an extendibility result for unipotent characters of groups of Lie type (Theorem 2.4) and it is finished the result that every group of Lie type is good for every prime \(p\geq 3\) different from the defining characteristic (Theorem 3.2).
Mathematics Subject Classification ID: 20C33
Mathematics Subject Classification ID: 20C15
zbMATH DE Number: 5376941
zbMATH Keywords: representations of groups
zbMATH Keywords: McKay conjecture
zbMATH Keywords: character bijections
zbMATH Keywords: numbers of complex irreducible characters
zbMATH Keywords: character degrees
zbMATH Keywords: finite groups of Lie type
zbMATH Keywords: unipotent characters
describes a project that uses: GAP
reviewed by: Alexandre A. Makhnev
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2008.06.033
OpenAlex ID: W2071688049
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DOI: 10.1016/J.JALGEBRA.2008.06.033
description: scientific article; zbMATH DE number 5376941