Primitive Characters and Permutation Characters of Solvable Groups
Representation Theory
2008-08-10 v2
Abstract
Let X be an irreducible, primitive complex character of the finite solvable group G, and let X* denote the complex conjugate character. If the degree X(1) is odd, then we show how to associate to X in a unique way, a conjugacy class of subgroups U of G for which X*X = (1_U)^G, the permutation character on the cosets of U. We investigate this situation and give a number of applications to properties of primitive characters of solvable and p-solvable groups.
Cite
@article{arxiv.0709.1209,
title = {Primitive Characters and Permutation Characters of Solvable Groups},
author = {Tom Wilde},
journal= {arXiv preprint arXiv:0709.1209},
year = {2008}
}
Comments
Attribution given for Theorem K, which it has been pointed out to me is the odd order case of a published result of P.A. Ferguson and I.M. Isaacs. A number of typos corrected, and a slight improvement made to Theorem J