On the degrees of irreducible factors of higher order

On Finite Groups With Two Irreducible Character Degrees

Some connections between powers of conjugacy classes and degrees of irreducible characters in solvable groups

‎Let $G$ be a finite group‎. ‎We say that the derived covering number of $G$ is finite if and only if there exists a positive integer $n$ such that $C^n=G'$ for all non-central conjugacy classes $C$ of $G$‎. ‎In this paper we characterize solvable groups $G$ in which the derived covering number is finite‎.‎ 

On minimal degrees of faithful quasi-permutation representations of nilpotent groups

By a quasi-permutation matrix, we mean a square non-singular matrix over the complex field with non-negative integral trace....

AFFINE SUBGROUPS OF THE CLASSICAL GROUPS AND THEIR CHARACTER DEGREES

In this paper we describe how the degrees of the irreducible characters of the affine subgroups of the classical groups under consideration can be found inductively. In [4] Gow obtained certain character degrees for all of the affine subgroups of the classical groups. We apply the method of Fischer to the above groups and, in addition to the character degrees given in [4], we obtain some ne...

On the degrees of irreducible factors of higher order Bernoulli polynomials

1. Introduction. In this paper, we generalize the current results on the p-Eisenstein behavior of first and higher order Bernoulli polynomials [4], [6–9], using the machinery of [1]. In so doing, we provide a broader framework for the known results, all of which are either immediate consequences or special cases of our more general results. Because of an explicit formula for the coefficients in...