Orthogonality of Cosets Relative to Irreducible Characters of Finite Groups

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 the irreducible characters of Camina triples

The Camina triple condition is a generalization of the Camina condition in the theory of finite groups. The irreducible characters of Camina triples have been verified in the some special cases. In this paper, we consider a Camina triple (G,M,N)  and determine the irreducible characters of G in terms of the irreducible characters of M and G/N.  

Notes on Representation Theory of Finite Groups

§1. Representations of finite groups 1 §1.1. Definition and Examples 1 §1.2. G-modules 3 §1.3. Mashke’s Theorem 4 §1.4. Schur’s Lemma 6 §1.5. One-dimensional representations 7 §1.6. Exercises 9 §2. Irreducible representations of finite groups 10 §2.1. Characters 10 §2.2. Basic operations on representations and their characters 11 §2.3. Schur’s orthogonality relations 12 §2.4. Decomposition of t...

Irreducible characters of Sylow $p$-subgroups of the Steinberg triality groups ${}^3D_4(p^{3m})$

‎‎Here we construct and count all ordinary irreducible characters of Sylow $p$-subgroups of the Steinberg triality groups ${}^3D_4(p^{3m})$.