On Degrees of Irreducible Brauer Characters

On Finite Groups With Two Irreducible Character Degrees

A Local Conjecture on Brauer Character Degrees of Finite Groups

Recently, a new conjecture on the degrees of the irreducible Brauer characters of a finite group was presented in [16]. In this paper we propose a ’local’ version of this conjecture for blocks B of finite groups, giving a lower bound for the maximal degree of an irreducible Brauer character belonging to B in terms of the dimension of B and well-known invariants like the defect and the number of...

Characters of Brauer's Centralizer Algebras

Brauer's centralizer algebras are finite dimensional algebras with a distinguished basis. Each Brauer centralizer algebra contains the group algebra of a symmetric group as a subalgebra and the distinguished basis of the Brauer algebra contains the permutations as a subset. In view of this containment it is desirable to generalize as many known facts concerning the group algebra of the symmetri...

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.‎ 

Burnside-Brauer Theorem and Character Products in Table Algebras

In this paper, we first show that the irreducible characters of a quotient table algebra modulo a normal closed subset can be viewed as the irreducible characters of the table algebra itself. Furthermore, we define the character products for table algebras and give a condition in which the products of two characters are characters. Thereafter, as a main result we state and prove the Burnside-Br...