Diameters of Degree Graphs of Nonsolvable Groups

Diameters of Degree Graphs of Nonsolvable Groups, II

Let G be a finite group and let cd(G) be the set of irreducible character degrees of G. The degree graph ∆(G) is the graph whose set of vertices is the set of primes that divide degrees in cd(G), with an edge between p and q if pq divides a for some degree a ∈ cd(G). It is shown using the degree graphs of the finite simple groups that if G is a nonsolvable group, then the diameter of ∆(G) is at...

Four-Vertex Degree Graphs of Nonsolvable Groups

For a finite group G, the character degree graph ∆(G) is the graph whose vertices are the primes dividing the degrees of the ordinary irreducible characters of G, with distinct primes p and q joined by an edge if pq divides some character degree of G. We determine all graphs with four vertices that occur as ∆(G) for some nonsolvable group G. Along with previously known results on character degr...

Connectedness of Degree Graphs of Nonsolvable Groups

The Complexity of the Equivalence Problem for Nonsolvable Groups

The equivalence problem for a group G is the problem of deciding which equations hold in G. It is known that for finite nilpotent groups and certain other solvable groups, the equivalence problem has polynomial-time complexity. We prove that the equivalence problem for a finite nonsolvable group G is co-NP-complete by reducing the k-coloring problem for graphs to the equivalence problem, where ...

Se p 20 05 A CHARACTERIZATION OF L 2 ( 2 f ) IN TERMS OF CHARACTER ZEROS ∗

The aim of this paper is to classify the finite nonsolvable groups in which every irreducible character of even degree vanishes on at most two conjugacy classes. As a corollary, it is shown that L2(2 f ) are the only nonsolvable groups in which every irreducible character of even degree vanishes on just one conjugacy class.