*Instructor:* Dr. József PELIKÁN

*Text: *I. Martin Isaacs, Character Theory of Finite Groups

*Prerequisite: *An introductory algebra course covering the basic
definitions and theorems on groups, rings and modules.

*Course description: * This is a course on the representation theory of
finite groups, with emphasis on the use and application of group
characters.

*Topics:*

Group representations, the group algebra. Schur's lemma. Maschke's
theorem. Wedderburn's theorem on semisimple algebras. Irreducible and
completely reducible representations.

Characters. The orthogonality relations. Determination of center,
commutator subgroup, normal subgroups from the character table.
Algebraic integers. Burnside's p^a q^b theorem. Theorems on character
degrees. Products of characters.

Induced representations and characters. M-groups, Taketa's theorem.
Frobenius groups. Frobenius' theorem on Frobenius kernels. TI-sets and
exceptional characters. Characterizations of groups by 2-Sylow
subgroups and centralizers of involutions.