J Austral Math Soc Ser A 57 pp81--102, 1994.

The p-Character Theory of Solvable Groups

I. M. Isaacs

Abstract

There is a deeper structure to the ordinary character theory of finite solvable groups than might at first be apparent. Much of this structure, which has no analog for general finite groups, becomes visible only when the characters of solvable groups are viewed from the perspective of a particular set p of prime numbers. This purely expository paper discusses the foundations of this p-theory and a few of its applications. Included are the definitions and essential properties of Gajendragadkar's p-special characters and their connections with the irreducible p partial 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.

1991 AMS Subject Classification: 20C15

Browse the article

Authors

I. M. Isaacs

Mathematics Department, University of Wisconsin, Madison WI 53706, USA.

mailto:isaacs@math.wisc.edu