A characterization of PGL (2,pn) by some irreducible complex character degrees

A CHARACTERIZATION OF PGL(2, p) BY SOME IRREDUCIBLE COMPLEX CHARACTER DEGREES

For a finite group G, let cd(G) be the set of irreducible complex character degrees of G forgetting multiplicities and X1(G) be the set of all irreducible complex character degrees of G counting multiplicities. Suppose that p is a prime number. We prove that if G is a finite group such that |G| = |PGL(2, p)|, p ∈ cd(G) and max(cd(G)) = p+1, then G ∼= PGL(2, p), SL(2, p) or PSL(2, p) × A, where ...

characterization of some simple $k_4$-groups by some irreducible complex character degrees

in this paper, we examine that some simple $k_4$-groups can be determined uniquely by their orders and one or two irreducible complex character degrees.

On Finite Groups With Two Irreducible Character Degrees

Prime Divisors of Irreducible Character Degrees

Let G be a finite group. We denote by ρ(G) the set of primes which divide some character degrees of G and by σ(G) the largest number of distinct primes which divide a single character degree of G. We show that |ρ(G)| ≤ 2σ(G) + 1 when G is an almost simple group. For arbitrary finite groups G, we show that |ρ(G)| ≤ 2σ(G) + 1 provided that σ(G) ≤ 2.

on finite groups with two irreducible character degrees