Bounds for Degrees and Sums of Degrees of Irreducible Characters of Some Classical Groups over Finite Fields

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.‎ 

AFFINE SUBGROUPS OF THE CLASSICAL GROUPS AND THEIR CHARACTER DEGREES

In this paper we describe how the degrees of the irreducible characters of the affine subgroups of the classical groups under consideration can be found inductively. In [4] Gow obtained certain character degrees for all of the affine subgroups of the classical groups. We apply the method of Fischer to the above groups and, in addition to the character degrees given in [4], we obtain some ne...

On Finite Groups With Two Irreducible Character Degrees

Character Degree Sums and Real Representations of Finite Classical Groups of Odd Characteristic

Let Fq be a finite field with q elements, where q is the power of an odd prime, and let GSp(2n, Fq) and GO±(2n, Fq) denote the symplectic and orthogonal groups of similitudes over Fq, respectively. We prove that every real-valued irreducible character of GSp(2n, Fq) or GO±(2n, Fq) is the character of a real representation, and we find the sum of the dimensions of the real representations of eac...

Groups whose Bipartite Divisor Graph for Character Degrees Has Five Vertices

Let $G$ be a finite group and $cd^*(G)$ be the set of nonlinear irreducible character degrees of  $G$. Suppose that $rho(G)$ denotes the set of primes dividing some element of $cd^*(G)$. The bipartite divisor graph for the set of character degrees which is denoted by $B(G)$, is a bipartite graph whose vertices are the disjoint union of $rho(G)$ and $cd^*(G)$, and a vertex $p in rho(G)$ is conne...