On Willems' conjecture on Brauer 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...

On Degrees of Irreducible Brauer Characters

Based on a large amount of examples, which we have checked so far, we conjecture that |G|p′ ≤ ∑ φ φ(1) 2 where p is a prime and the sum runs through the set of irreducible Brauer characters in characteristic p of the finite group G. We prove the conjecture simultaneously for p-solvable groups and groups of Lie type in the defining characteristic. In non-defining characteristics we give asymptot...

On the Navarro-willems Conjecture for Blocks of Finite Groups

Let G be a finite group. For a prime p and a p-block B of G, we denote by Irr(B) the set of complex irreducible characters of G that belong to B. It was conjectured by Navarro and Willems [NW] that if for blocks Bp and Bq of G at different primes p, q we have an equality Irr(Bp) = Irr(Bq) then |Irr(Bp)| = 1. But then the first author of the present article found that the extension group 6.A7 of...

On Finite Groups With Two Irreducible Character Degrees

on bipartite divisor graph for character degrees

‎the concept of the bipartite divisor graph for integer subsets has been considered in [‎m‎. ‎a‎. ‎iranmanesh and c‎. ‎e‎. ‎praeger‎, ‎bipartite divisor graphs for integer subsets‎, ‎{em graphs combin.}‎, ‎{bf 26} (2010) 95--105‎.]‎. ‎in this paper‎, ‎we will consider this graph for the set of character degrees of a finite group $g$ and obtain some properties of this graph‎. ‎we show that if $g...