Search results for "character"
showing 10 items of 2956 documents
Irreducible induction and nilpotent subgroups in finite groups
2019
Suppose that $G$ is a finite group and $H$ is a nilpotent subgroup of $G$. If a character of $H$ induces an irreducible character of $G$, then the generalized Fitting subgroup of $G$ is nilpotent.
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.
Brauer characters with cyclotomic field of values
2008
It has been shown in an earlier paper [G. Navarro, Pham Huu Tiep, Rational Brauer characters, Math. Ann. 335 (2006) 675–686] that, for any odd prime p, every finite group of even order has a non-trivial rational-valued irreducible p-Brauer character. For p=2 this statement is no longer true. In this paper we determine the possible non-abelian composition factors of finite groups without non-trivial rational-valued irreducible 2-Brauer characters. We also prove that, if p≠q are primes, then any finite group of order divisible by q has a non-trivial irreducible p-Brauer character with values in the cyclotomic field Q(exp(2πi/q)).
Characters of 𝑝’-degree with cyclotomic field of values
2006
If p p is a prime number and G G is a finite group, we show that G G has an irreducible complex character of degree not divisible by p p with values in the cyclotomic field Q p \mathbb {Q}_p .
A self-centralizing characteristic subgroup
1989
AbstractIn this note we introduce a self-centralizing characteristic subgroup, associated with quasinilpotent injectors, of a finite group.
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.
A metric characterization of Carnot groups
2013
We give a short axiomatic introduction to Carnot groups and their subRiemannian and subFinsler geometry. We explain how such spaces can be metrically described as exactly those proper geodesic spaces that admit dilations and are isometrically homogeneous.
Self-improvement of pointwise Hardy inequality
2019
We prove the self-improvement of a pointwise p p -Hardy inequality. The proof relies on maximal function techniques and a characterization of the inequality by curves.
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…