Primitive characters of subgroups of M-groups
type: Item
instance of: scholarly article
title: Primitive characters of subgroups of M-groups
zbMATH Open document ID: 0824.20008
DOI: 10.1007/BF02571914
author: Gabriel Navarro
published in: Mathematische Zeitschrift
publication date: 1995-10-30T00:00:00Z
full work available at URL: https://eudml.org/doc/174739
review text: If \(G\) is a monomial group, it has been conjectured that Hall subgroups of \(G\) are monomial. Recently, some idea is taking form: perhaps, even the Hall subgroup normalizers are monomial. Toward this stronger result we prove that the irreducible primitive characters of Hall subgroup normalizers of M-groups are linear. One of the reasons why M-groups are so difficult to understand is because, as shown by E. C. Dade, every solvable group is a subgroup of some M-group. The techniques used in this paper allow us to give a restriction on Dade's theorem: If \(G\) is a monomial group and \(H\) is a subgroup of \(G\) with \(\pi\)-index, then every primitive character of \(H\) has \(\pi\)-degree. For instance, as a consequence of this, \(\text{SL}(2,3)\) cannot have odd index in an M- group.
Mathematics Subject Classification ID: 20C15
Mathematics Subject Classification ID: 20D20
Mathematics Subject Classification ID: 20D60
zbMATH DE Number: 778955
zbMATH Keywords: monomial groups
zbMATH Keywords: Hall subgroups
zbMATH Keywords: irreducible primitive characters
zbMATH Keywords: M- groups
zbMATH Keywords: solvable groups
zbMATH Keywords: \(\pi\)-index
zbMATH Keywords: \(\pi\)-degree
reviewed by: J. Navarro
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 778955