Certain monomial characters of \(p'\)-degree.
type: Item
instance of: scholarly article
title: Certain monomial characters of \(p'\)-degree.
zbMATH Open document ID: 1263.20006
author: Gabriel Navarro
author: Carolina Vallejo Rodríguez
published in: Archiv der Mathematik
publication date: 2012-12-19T00:00:00Z
review text: Let \(G\) be a \(p\)-solvable finite group, let \(P\) be a Sylow \(p\)-subgroup of \(G\), and assume that \(N_G(P)/P\) has odd order. Let \(\mathbb Q_{p^a}\) be the field of rational numbers extended by a primitive \(p^a\)-th root of one. Let \(\chi\) be an irreducible character of \(G\) whose degree is not divisible by \(p\), and whose values lie in \(\mathbb Q_{p^a}\). It is proved in the paper that \(\chi\) is then induced from a linear character of some subgroup of \(G\) whose values are in \(\mathbb Q_{p^a}\). Furthermore, this linear character is unique up to \(G\)-conjugacy.
reviewed by: Alexandre Turull
Mathematics Subject Classification ID: 20C15
Mathematics Subject Classification ID: 20D20
zbMATH DE Number: 6116961
zbMATH Keywords: rational characters
zbMATH Keywords: monomial characters
zbMATH Keywords: characters of finite groups
zbMATH Keywords: \(p\)-solvable groups
MaRDI profile type: Publication
full work available at URL: s00013-012-0449-0
OpenAlex ID: W2057927981
cites work: Real‐Valued Characters of Solvable Groups
cites work: Characters of solvable groups induced by linear characters of Hall subgroups
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cites work: Q3413656
cites work: Hall Subgroup Normalizers and Character Correspondences in M-Groups
cites work: Rationality and Sylow 2-subgroups
cites work: Odd character correspondences in solvable groups.
DOI: 10.1007/S00013-012-0449-0
description: scientific article; zbMATH DE number 6116961