The character values of the irreducible constituents of a transitive permutation representation
type: Item
instance of: scholarly article
title: The character values of the irreducible constituents of a transitive permutation representation
zbMATH Open document ID: 1007.20007
author: Gerhard O. Michler
author: Michael Weller
published in: Archiv der Mathematik
publication date: 2002-09-10T00:00:00Z
review text: Let \(G\) be a finite group and let \(M\) be a given subgroup of \(G\). The permutation character of \(G\) on \(M\) over the complex field \(\mathbb{C}\) is denoted by \((1_M)^G\). In the paper under review the authors develop a method to find all the irreducible ordinary characters \(\chi_r\) occurring as a constituent of \((1_M)^G\). They also determine the multiplicity of each \(\chi_r\) in \((1_M)^G\). They illustrate the method for Janko's sporadic group \(G=J_1\) and \(M=C_G(z)\), where \(z\) is an involution in \(G\).
reviewed by: M. R. Darafsheh
Mathematics Subject Classification ID: 20C15
Mathematics Subject Classification ID: 20C34
zbMATH DE Number: 1798904
zbMATH Keywords: finite groups
zbMATH Keywords: permutation characters
zbMATH Keywords: irreducible ordinary characters
zbMATH Keywords: constituents
zbMATH Keywords: multiplicities
zbMATH Keywords: Janko's sporadic group \(J_1\)
MaRDI profile type: Publication
full work available at URL: s00013-002-8266-5
OpenAlex ID: W2024901017
DOI: 10.1007/S00013-002-8266-5
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description: scientific article; zbMATH DE number 1798904