‎in this paper‎, ‎we obtain the dimensions of symmetry classes of polynomials associated with‎ ‎the irreducible characters of the dihedral group as a subgroup of‎ ‎the full symmetric group‎. ‎then we discuss the existence of o-basis‎ ‎of these classes‎.

‎In this paper‎, ‎we obtain the dimensions of symmetry classes of polynomials associated with‎ ‎the irreducible characters of the dihedral group as a subgroup of‎ ‎the full symmetric group‎. ‎Then we discuss the existence of o-basis‎ ‎of these classes‎.

0.1. Let G be a connected reductive algebraic group defined over a finite field Fq and let G(Fq) be the finite group of all Fq-rational points of G. We would like to present here a strategy for computing the character table of G(Fq) , under the assumption that p, the characteristic of Fq , is sufficiently large. We can assume that G has a simply connected derived group. Indeed, in the general c...

We study the finite groups G with a faithful irreducible character whose square is a linear combination of algebraically conjugate irreducible characters of G. In conclusion, we offer another proof of one theorem of Isaacs-Zisser. There are a few papers treating the finite groups possessing an irreducible character whose powers are linear combinations of appropriate irreducible characters, for ...

Let G be a finite group, p a prime, and P a Sylow p-subgroup of G. Several recent refinements of the McKay conjecture suggest that there should exist a bijection between the irreducible characters of p′-degree of G and the irreducible characters of p′-degree of NG(P ), which preserves field of values of correspondent characters (over the p-adics). This strengthening of the McKay conjecture has ...

Computational methods for finding the character table of a finite group require a stock of reducible characters and techniques for decomposing these characters into irreducible characters. A method for generating reducible characters from a representation of a group is proposed. Several new techniques for computing the irreducible decompositions of a set of characters are given; these technique...

the aim of this note is to characterize the finite groups in which all non-linear irreducible characters have distinct zero entries number.