I.M. Isaacs,: Character Theory of Finite Groups - AMS Chelsea Publishing
Learning Objectives
Fundamental concepts of the character theory of finite groups. Applications to group theory.
Prerequisites
Fundamentals in group theory, ring theory and linear algebra.
Teaching Methods
Lectures
Type of Assessment
Oral exam.
Course program
Albegras and modules. Schur's Lemma. Module theory. Semisimple algebras. Theorems of Maschke and Wedderburn.
Linear representations and characters. Orthogonality relations.
Burnside theorem. Character degrees. Restriction and induction.
M- groups; Taketa's theorem.
Permutation characters. Artin's theorem.
Clifford theory and applications.