Search results for "Irreducible element"

Irreducible Representations of Periodic Finitary Linear Groups

1996

Groups whose real irreducible characters have degrees coprime to p

2012

Abstract In this paper we study groups for which every real irreducible character has degree not divisible by some given odd prime p .

Rational irreducible characters and rational conjugacy classes in finite groups

2007

We prove that a finite group G G has two rational-valued irreducible characters if and only if it has two rational conjugacy classes, and determine the structure of any such group. Along the way we also prove a conjecture of Gow stating that any finite group of even order has a non-trivial rational-valued irreducible character of odd degree.

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.

q-Fock Space Representations of the q-Lorentz Algebra and Irreducible Tensors

1993

We present the q-deformation of the Lorentz algebra, with Hopf structure, in terms of four independent harmonic oscillators. The explicit realization of the q-Fock space is given and the irreducible finite-dimensional representations of so(1,3)q are described and characterized by its two q-Casimir operators. The concept of irreducible q-Lorentz tensor is also introduced. The analysis is made for a real deformation parameter.

Deformation modes according to irreducible representations

2001

Abstract A method for obtaining distortion fields in a crystal from a given irreducible representation of the underlying space group is described in Ref.[1]. The method is based on projection operators of the group theory, it is graphically oriented and thus calculation free. As an example (Space group P421m)complete sets of representation matrices ara analytically calculated for all irreducible representations which correspond to all wave vectors of the form k= (q, q, 0). Linear independent atomic displacement modes in the (3×3×1) supercell, which are induced by the two irreducible representations with k = (1/3,1/3,0) are explicitly determined: the obtained atomic displacement fields are p…