Search results for "Characters"

Brauer's fixed-point-formula as a consequence of Thompson's order-formula

1991

The number of lifts of a Brauer character with a normal vertex

2011

AbstractIn this paper we examine the behavior of lifts of Brauer characters in p-solvable groups. In the main result, we show that if φ∈IBr(G) has a normal vertex Q and either p is odd or Q is abelian, then the number of lifts of φ is at most |Q:Q′|. As a corollary, we prove that if φ∈IBr(G) has an abelian vertex subgroup Q, then the number of lifts of φ in Irr(G) is at most |Q|.

Complex group algebras of finite groups: Brauer’s Problem 1

2005

Brauer’s Problem 1 asks the following: what are the possible complex group algebras of finite groups? It seems that with the present knowledge of representation theory it is not possible to settle this question. The goal of this paper is to announce a partial solution to this problem. We conjecture that if the complex group algebra of a finite group does not have more than a fixed number m m of isomorphic summands, then its dimension is bounded in terms of m m . We prove that this is true for every finite group if it is true for the symmetric groups.

Some problems about products of conjugacy classes in finite groups

2020

[EN] We summarize several results about non-simplicity, solvability and normal structure of finite groups related to the number of conjugacy classes appearing in the product or the power of conjugacy classes. We also collect some problems that have only been partially solved.

On the orders of zeros of irreducible characters

2009

Let G be a finite group and p a prime number. We say that an element g in G is a vanishing element of G if there exists an irreducible character χ of G such that χ (g) = 0. The main result of this paper shows that, if G does not have any vanishing element of p-power order, then G has a normal Sylow p-subgroup. Also, we prove that this result is a generalization of some classical theorems in Character Theory of finite groups. © 2008 Elsevier Inc. All rights reserved.

Brauer characters and coprime action

2016

Abstract It is an open problem to show that under a coprime action, the number of invariant Brauer characters of a finite group is the number of the Brauer characters of the fixed point subgroup. We prove that this is true if the non-abelian simple groups satisfy a stronger condition.

Group graded algebras and multiplicities bounded by a constant

2013

AbstractLet G be a finite group and A a G-graded algebra over a field of characteristic zero. When A is a PI-algebra, the graded codimensions of A are exponentially bounded and one can study the corresponding graded cocharacters via the representation theory of products of symmetric groups. Here we characterize in two different ways when the corresponding multiplicities are bounded by a constant.

Quotients of Fermat curves and a Hecke character

2005

AbstractWe explicitly identify infinitely many curves which are quotients of Fermat curves. We show that some of these have simple Jacobians with complex multiplication by a non-cyclotomic field. For a particular case we determine the local zeta functions with two independent methods. The first uses Jacobi sums and the second applies the general theory of complex multiplication, we verify that both methods give the same result.

Characterizing normal Sylow p-subgroups by character degrees

2012

Abstract Suppose that G is a finite group, let p be a prime and let P ∈ Syl p ( G ) . We prove that P is normal in G if and only if all the irreducible constituents of the permutation character ( 1 P ) G have degree not divisible by p.

Quadratic characters in groups of odd order

2009

Abstract We prove that in a finite group of odd order, the number of irreducible quadratic characters is the number of quadratic conjugacy classes.