Title: Character Theory of Finite Groups
Lecturer:
Don Taylor
The University of Sydney
Abstract:
Gauss introduced (and named) characters in connection with the
composition of binary quadratic forms. Dirichlet, Dedekind and then
Frobenius rephrased the ideas of Gauss in terms of what are now called
characters of abelian groups. Frobenius, Burnside, Schur and Brauer
went on to develop character theory as an important tool for the study
of the structure of finite groups.
There are still intriguing open questions! For example, the McKay
conjecture: a finite group G and the normaliser of a Sylow p-subgroup
of G have the same number of characters of degree not divisible by p.
The lecture titles are:
(1) Introduction to character theory.
(2) Burnside's theorem on groups of order p^a q^b.
(3) Induced characters and Frobenius reciprocity.
(4) An elementary approach to the characters of the symmetric groups.