Relative projective monomial groups
type: Item
instance of: scholarly article
zbMATH Open document ID: 0968.20004
author: EunMi Choi
publication date: 2001-03-19T00:00:00Z
Mathematics Subject Classification ID: 20C15
Mathematics Subject Classification ID: 20C25
zbMATH DE Number: 1579144
zbMATH Keywords: linear representations
zbMATH Keywords: relative monomial characters
zbMATH Keywords: projective Clifford theory
zbMATH Keywords: relative projective monomial characters
MaRDI profile type: Publication
title: Relative projective monomial groups
published in: Communications of the Korean Mathematical Society
review text: Clifford's theory for linear representations (or characters) is generally very well known; see for instance Chapter 6 in \textit{I. M. Isaacs}' book ``Character theory of finite groups'' [Dover, New York (1994; Zbl 0849.20004)]. It is of some importance to know whether \(\chi\in\text{Irr}(G)\) satisfies \(\vartheta^G=\chi\) and \(\vartheta_N\in\text{Irr}(N)\), where \(N\) is a normal subgroup of \(G\). If so, we say that \(\chi\) is a relative monomial character with respect to \(N\).NEWLINENEWLINENEWLINEIn this paper things are recasted in the realm of projective Clifford theory and so-called relative projective monomial characters with respect to a normal subgroup. Things run certainly not so smoothly as in the linear representations case, and the results obtained are an important contribution to extend well-established results on monomial characters to results on projective monomial characters.
reviewed by: Robert W. van der Waall
description: scientific article