The number of lifts of a Brauer character with a normal vertex.
type: Item
instance of: scholarly article
title: The number of lifts of a Brauer character with a normal vertex.
zbMATH Open document ID: 1238.20011
author: James P. Cossey
author: Mark L. Lewis
author: Gabriel Navarro
published in: Journal of Algebra
publication date: 2011-05-16T00:00:00Z
review text: Let \(p\) be a prime, let \(G\) be a \(p\)-solvable group, and let \(\varphi\) be an irreducible \(p\)-modular character of \(G\). By a theorem of Fong and Swan, there exists an ordinary irreducible character \(\chi\) of \(G\) such that the restriction of \(\chi\) to the \(p\)-regular conjugacy classes of \(G\) is equal to \(\varphi\). In this case, \(\chi\) is called a lift of \(\varphi\). The main result of the paper is that if the vertex \(Q\) of \(\varphi\) is normal in \(G\) and either \(p\) is odd or \(Q\) is Abelian, then the number of lifts of \(\varphi\) is bounded above by the index \([Q:Q']\). In particular, if \(Q\) is Abelian the number of lifts of \(\varphi\) is at most \(|Q|\).
Mathematics Subject Classification ID: 20C20
Mathematics Subject Classification ID: 20C15
zbMATH DE Number: 5888505
zbMATH Keywords: irreducible Brauer characters
zbMATH Keywords: finite \(p\)-solvable groups
zbMATH Keywords: character lifts
reviewed by: Frauke Bleher
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2010.07.044
OpenAlex ID: W1989969483
cites work: Bounds on the number of lifts of a Brauer character in a \(p\)-solvable group.
cites work: Character theory of finite groups
cites work: Q4103728
cites work: Q4012102
cites work: Weights and vertices for characters of \(\pi\)-separable groups
cites work: Q4273959
cites work: Q4387775
cites work: Actions and characters in blocks.
cites work: Modularly irreducible characters and normal subgroups.
DOI: 10.1016/J.JALGEBRA.2010.07.044
Recommended article: Lifts of Brauer characters in characteristic two
Recommended article: Bounds on the number of lifts of a Brauer character in a \(p\)-solvable group.
Recommended article: Lifts of partial characters with respect to a chain of normal subgroups.
Recommended article: Brauer character degrees and Sylow normalizers
Recommended article: Brauer characters relative to a normal subgroup
Recommended article: On degrees of irreducible Brauer characters
Recommended article: Brauer characters and normal Sylow \(p\)-subgroups
Recommended article: Sylow normalizers and Brauer character degrees
Recommended article: Brauer characters of $q’$- degree
Recommended article: Groups whose Brauer-characters are liftable
description: scientific article; zbMATH DE number 5888505