Nonabelian fully-ramified sections

TL;DR: In this paper, it was shown that the Taketa inequality is valid for solvable groups with at most five character degrees and that the derived length of G is at most 5.

TL;DR: In this article, the authors examined the character degree set of a set X of positive integers that includes 1 and showed that the set of irreducible character degrees of X is a finite group whose degree set cd G s x 1 x g Irr G equals X.

TL;DR: In this article, it was shown that if G is an M-group and S is a subnormal subgroup of G, then the primitive characters of S all have degrees that are powers of 2.

TL;DR: The character theory of solvable groups has been studied extensively in the literature (see as mentioned in this paper for a survey of the main results of character theory in solvable group theory). But the main result in this paper is based on the going down theorem (Theorem 6.18 of [9] ).