Irreducible character degrees and normal subgroups
Group Theory
2009-09-25 v1
Abstract
Let N be a normal subgroup of a finite group G and consider the set cd(G|N) of degrees of irreducible characters of G whose kernels do not contain N. A number of theorems are proved relating the set cd(G|N) to the structure of N. For example, if N is solvable, its derived length is bounded above by a function of |cd(G|N)|. Also, if |cd(G|N)| is at most 2, then N is solvable and its derived length is at most |cd(G|N)|. If G is solvable and |cd(G|N)| = 3, then the derived length of N is at most 3.
Cite
@article{arxiv.math/9702233,
title = {Irreducible character degrees and normal subgroups},
author = {I. M. Isaacs and Greg Knutson},
journal= {arXiv preprint arXiv:math/9702233},
year = {2009}
}