Number of modular character degrees and lengths for solvable groups

Bounding the Number of Character Degrees of a Solvable Group

A difficult problem in the character theory of solvable groups is to show that the number c.d. (G) of irreducible character degrees of a solvable group G is equal to or greater than d.l. (G), the derived length of G. Isaacs [4] has shown that d.l. (G) ^ 3 c.d. (G)-2 for every solvable group. Berger [1] subsequently proved that d.l. (G) < c.d. (G) when | G | is odd. This problem belongs to the c...

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...

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 Finite Groups With Two Irreducible Character Degrees

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 new ch...