FINITE THEORY

(1)

CHARACTER THEORY

^OF

FINITE GROUPS

SOMMERSEMESTER ²⁰²⁰

CAROLINE LASSUEUR

TU KAISERSLAUTERN

(2)

CHARACTER

THEORY ^OF

FINITE GROUPS

552020 ^BEFORE GroupTheory A.

^AND ^AFTER ^Linear

Algebra

(Aasttinf Algebra) ( ^GDM)

Character

Theory

therM.sc ^.Lectures^: Representation

Fachpraktikum

B.sc .&M .se

. Group Theory Theory ¹^MSc^.⁾ ⁽^with ^GAPIMAGMA⁾ ^Theses

. Cohomology

of

Groups

. Lie Algebras

(3)

CHARACTER

THEORY ^OF

FINITE GROUPS

552020 INTRODUCTION B.

Aims

of

^the ^lecture ^:

Character

Tables

of finite _groups

^: ^What ^are

they

^?

Elementary

^methods ^to _compute ^them ^.

What

information

^about

finite

_groups

do they contain ? Give a

proof of

^:

Burnside 's paqb ^- Theorem^:

Letpqbeprime

^numbers ^and ^let ^a ^,bElNo ^.

(

^ggn ) ^Then ^any

finite

_group

of

^order ^paq^' ^is ^soluble ^.

(4)

CHARACTER

THEORY ^OF

FINITE GROUPS

552020 ^PROGRAMME

^. ^Linear

C.

representations

of finite ^The

_groups^main ^topics

^of

^the

^lecture

^are ^:

. Characters

of

representations

. The character table

It

. Burnside^'s paqb^.Theorem I Induction and restriction

I ^. Brauer 's

Characterization of

^characters ^.

( If

^time ^{permits )}

FINITE THEORY

CHARACTER THEORY

FINITE GROUPS

CHARACTER

552020 BEFORE GroupTheory A.

Algebra

Theory

Fachpraktikum

of

CHARACTER

552020 INTRODUCTION B.

of

Character

of finite groups

they

Elementary

information

finite

proof of

Letpqbeprime

(

finite

of

CHARACTER

552020 PROGRAMME

C.

of finite The

of

lecture

of

It

Characterization of

( If

552020 ^BEFORE GroupTheory A.

of finite _groups

552020 ^PROGRAMME

of finite ^The

^of

^lecture