Groups whose character degree graph has diameter three
Group Theory
2016-07-19 v1
Abstract
Let be a finite group, and let denote the \emph{prime graph} built on the set of degrees of the irreducible complex characters of . It is well known that, whenever is connected, the diameter of is at most . In the present paper, we provide a description of the finite solvable groups for which the diameter of this graph attains the upper bound. This also enables us to confirm a couple of conjectures proposed by M.L. Lewis.
Cite
@article{arxiv.1607.05038,
title = {Groups whose character degree graph has diameter three},
author = {Carlo Casolo and Silvio Dolfi and Emanuele Pacifici and Lucia Sanus},
journal= {arXiv preprint arXiv:1607.05038},
year = {2016}
}