CHARACTER THEORY OF FINITE GROUPSSOMMERSEMESTER 2017

CAROLINE LASSUEUR

TU KAISERSLAUTERN

CHARACTER THEORY OFFINITE GROUPS 552017

A. ORGANISATION

• LECTURE : Tuesdays 10:00 - 11:30 ( 14×1

• EXERCISES : Fridays 13:45 - 15:15 ( 7x ) .Start :

2nd Week

Assistant : Inga Schwabrow

Exercise Sheets : online : Wednesdays 14:00

( Weeks : 1,2, 4. 6,8 . 10,12 )

Due date : Wednesdays 14:00

( Weeks : 2,4 , 6,8,

10.12.14 )

• SCHEINE : Toobtainanllbungsscheinyouneed : - 50% of the points on the 7- Exercise Sheets altogether

;1 point in 2 Exercises out '

of 4 in each Ex .Sheet 1-7

attendance to Exercise Classes + presenting 1 solutionon the board .

CHARACTER THEORY OFFINITE GROUPS 552017

B. BEFORE AND AFTER

GroupTheory Linear Algebra( AGSTE # Algebra ) ( GDM )

Character

Theory

therM.sc . Lectures : Representation Fachpraktikum B.sc .&M .se. Group Theory Theory 1 M.sc

.) (with GAPIMAGMA ) Theses. Cohomology of Groups. Lie Algebras

www.ams.org/msc/msc2010.pdf

J.H. CONWAY, R.T. CURTIS, S.P. NORTON, R. PARKER, R.A. WILSON,

Atlas of Finite Groups. Clarendon Press, Oxford, 1985.

CHARACTER THEORY OFFINITE GROUPS 552017

C. INTRODUCTION

(1.) Character Theory in the 2010 Mathematics Subject Classification

(2.) The ATLAS OF FINITE GROUPS

.

CHARACTER THEORY OFFINITE GROUPS 552017

C. INTRODUCTION

(3.) Aims of the lecture :

Character Tables of finite groups : What are they ?

Elementary methods to compute them .

What information about finite groupsdo 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 .

CHARACTER THEORY OFFINITE GROUPS SS 2017

D.PROGRAMME. Linear representations of finite groups

.Characters of representations

.the character table

It.

Burnside 's paqb . . Theorem

I Induction and restriction

TI . Brauer 's Characterization of characters.