Character degree graphs that are complete graphs

By M. Bianchi, D. Chillag, M. Lewis, E. Pacifici. 2006

150 citations recorded by the source corpus.

Let G be a finite group, and write cd(G) for the set of degrees of irreducible characters of G. We define F(G) to be the graph whose vertex set is cd(G) - {1}, and there is an edge between a and b if (a, b) > 1. We prove that if Γ(G) is a complete graph, then G is a solvable group.

Subfields: Artificial Intelligence, Discrete Mathematics and Combinatorics, Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/ad6b2c53611f9759de379ce0cffe72a9418e7cd2

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

1. S. Dolfi
2. Lucia Sanus
3. Pablo Spiga
4. E. Pacifici

Citations in the corpus

• On the orders of zeros of irreducible characters (2009, background): “The following proposition, which appears as Lemma 5 in [1], will turn out to be useful in handling the case when a nonabelian simple group fails to have irreducible characters of p-defect zero.”