Sets of $p$-powers as irreducible 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.

Some connections between powers of conjugacy classes and degrees of irreducible characters in solvable groups

‎Let $G$ be a finite group‎. ‎We say that the derived covering number of $G$ is finite if and only if there exists a positive integer $n$ such that $C^n=G'$ for all non-central conjugacy classes $C$ of $G$‎. ‎In this paper we characterize solvable groups $G$ in which the derived covering number is finite‎.‎ 

A Closed Character Formula for Symmetric Powers of Irreducible Representations

We prove a closed character formula for the symmetric powers SNV (λ ) of a fixed irreducible representation V (λ ) of a complex semi-simple Lie algebra g by means of partial fraction decomposition. The formula involves rational functions in rank of g many variables which are easier to determine than the weight multiplicities of SNV (λ ) themselves. We compute those rational functions in some in...

Finite p-groups with few non-linear irreducible character kernels

Abstract. In this paper, we classify all of the finite p-groups with at most three non linear irreducible character kernels.