Character Correspondences, Degrees, and Derived Length in Solvable Groups

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

Character Sheaves on Neutrally Solvable Groups

Let G be an algebraic group over an algebraically closed field k of characteristic p > 0. In this paper we develop the theory of character sheaves on groups G such that their neutral connected components G◦ are solvable algebraic groups. For such algebraic groups G (which we call neutrally solvable) we will define the set CS(G) of character sheaves on G as certain special (isomorphism classes o...

On Solvable Groups of Arbitrary Derived Length and Small Commutator Length

Let G be a group and G′ its commutator subgroup. Denote by c G the minimal number such that every element ofG′ can be expressed as a product of at most c G commutators. A group G is called a c-group if c G is finite. For any positive integer n, denote by cn the class of groups with commutator length, c G n. Let Fn,t 〈x1, . . . , xn〉 andMn,t 〈x1, . . . , xn〉 be, respectively, the free nilpotent ...