Generalized Clifford correspondences for group characters
type: Item
instance of: scholarly article
title: Generalized Clifford correspondences for group characters
zbMATH Open document ID: 0535.20003
DOI: 10.1007/BF01246941
author: Everett C. Dade
published in: Mathematische Zeitschrift
publication date: 1984-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/173564
review text: Suppose that \(\phi\) is a complex irreducible character of a normal subgroup N of a finite group G. Clifford Theory tells us that induction is a bijection of the set \(Irr(G\{\phi \}| \phi)\) (of all irreducible characters \(\chi\) of the stabilizer \(G\{ \phi\}\) of \(\phi\) in G such that \(\chi\) lies over \(\phi)\) onto the corresponding set \(Irr(G| \phi)\) for G. In this paper we consider the consequences of the existence of such a bijection for an arbitrary irreducible character of an arbitrary subgroup of G. More specifically, we define an inductive source for G to be any irreducible character \(\phi\) of a subgroup of G such that induction is a bijection of \(Irr(G\{\phi \}| \phi)\) onto \(Irr(G| \phi),\) and the associated IS-correspondent \(\psi\{ \phi\}\) of any \(\psi \in Irr(G| \phi)\) to be the unique character in \(Irr(G\{\phi \}| \phi)\) from which \(\psi\) is induced. We show that these sources and correspondents have most of the usual properties of irreducible characters of normal subgroups and the associated Clifford correspondents, including the correct ''compounding properties''. Indeed the IS-correspondents are much easier to handle then (repeated) Clifford correspondents due to their closure under most constructions. We also show that IS-correspondents reduce to repeated Clifford correspondents in certain interesting cases of nilpotent and odd normal subgroups.
Mathematics Subject Classification ID: 20C15
zbMATH DE Number: 3849466
zbMATH Keywords: complex irreducible characters
zbMATH Keywords: Clifford theory
zbMATH Keywords: bijections
zbMATH Keywords: sources
zbMATH Keywords: irreducible characters of normal subgroups
zbMATH Keywords: Clifford correspondents
zbMATH Keywords: IS- correspondents
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3849466