Search results for "Character table"

Field of values of cut groups and k-rational groups

2022

Abstract Motivated by a question of A. Bachle, we prove that if the field of values of any irreducible character of a finite group G is imaginary quadratic or rational, then the field generated by the character table Q ( G ) / Q is an extension of degree bounded in terms of the largest alternating group that appears as a composition factor of G. In order to prove this result, we extend a theorem of J. Tent on quadratic rational solvable groups to nonsolvable groups.

On zeros of characters of finite groups

2018

We survey some results concerning the distribution of zeros in the character table of a finite group and its influence on the structure of the group itself.

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…

Characters and generation of Sylow 2-subgroups

2021

Decomposition numbers and local properties

2020

Abstract If G is a finite group and p is a prime, we give evidence that the p-decomposition matrix encodes properties of p-Sylow normalizers.