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The π-character theory of solvable groups

Part of: Representation theory of groups

Published online by Cambridge University Press:  09 April 2009

I. M. Isaacs
I. M. Isaacs
Affiliation:
Mathematics Department, University of Wisconsin, Madison WI 53706, USA, e-mail: isaacs@math.wisc.edu
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Abstract

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There is a deeper structure to the ordinary character theory of finite solvable groups than might at first be apparent. Mauch of this structure, which has no analog for general finite gruops, becomes visible onyl when the character of solvable groups are viewes from the persepective of a particular set π of prime numbers. This purely expository paper discusses the foundations of this πtheory and a few of its applications. Included are the definitions and essential properties of Gajendragadkar's π-special characters and their connections with the irreducible πpartial characters and their associated Fong characters. Included among the consequences of the theory discussed here are applications to questions about the field generated by the values of a character, about extensions of characters of subgroups and about M-groups.

MSC classification

Secondary: 20C15: Ordinary representations and characters
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 57 , Issue 1 , August 1994 , pp. 81 - 102
Copyright
Copyright © Australian Mathematical Society 1994

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