GROUPS 552018

(1)

ELTHLTMOLOGY

^OF

GROUPS 552018

u

CAROLINE LASSUEUR TU KAISERSLAUTERN

(2)

ELTHTMLTLLTGY OF GROUPS 552018

A. ORGANISATION

• LECTURE ^: _Tuesdays

11:45

^-

13:15

^• ^EXERCISES^:

^Wednesdays

^Wednesdays ^13:45^10:00 ^-^- ^15:15

11:30

Exercise Sheets^Assistant^: ^Patrick^: ^Wegener^online ^: _Tuesdays

Due date^: Tuesdays

10:00

Start ^: _{2nd Week} ^. ^{1st Week} ^: _optional _, short tutorial ongrouptheory

(3)

ETHLTMUTIGY OF GROUPS 552018

B.

BEFORE

AND AFTER

GroupTheory

^Linear

Algebra

(AGSTE # Algebra) ( ^GDM)

Cohomology

of

Groups

.

Connections ^to other M.sc^. Lectures^:

. RepresentationTheory Reading ^Courses ^M.sc ^.

ilie Algebras

i.

Seminars

Thesis

.

Algebraic

^Topology

(4)

EEHOMOLOGY OF GROUPS 552018

C.

INTRODUCTION

(

^Aims^Learn^{Main Aim}

^of

^about^the

1.)

^: ^lectureHomological^do

^Group

^: Algebra^Theory ^viaândââ ^modern

specific ^approach Cohomology ^Theory

Work with

the language

of

^Category

Theory

^and ^Universal Properties

Connections between

central extensions of _groups

( 1 ^→ A ^> E±± ^> ^G ^- ^> ¹ with HAKZCE ⁾ ) and cohomology ⁽ ^H^' ^and ^H2⁾ ^.

+ consequences

for

_group

theory

^: ^: Classifications of small

finite

_group^,

Schur

multiplier

. Simple

/

_quasi^-

simple

_groups

(5)

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.

ELTHLTMELLTGY OF GROUPS 552018

C.

INTRODUCTION

( ^Cohomology

2.) ^of

^groups ^{and the} 2010 Mathematics

Subject Classification

(

^The

3.)

^ATLAS ^OF ^FINITE ^GROUPS .

(6)

ETHNOLOGY OF GROUPS 552018

D. PROGRAMME

We will treat the following topics^:

. Backgrounds ^on _group theory

}

^read by ^P^. Wegener

. Backgrounds ^on ^module theory

.

Homological Algebra

K

^I

^Homology ^Cohomology

^and^and

^cohomology ^group ^extensions ^of

^groups

I. The

Schur multiplier

^and

central extensions

I.

Projective

Representations

GROUPS 552018

ELTHLTMOLOGY

GROUPS 552018

11:45

13:15

Wednesdays

11:30

10:00

BEFORE

GroupTheory

Algebra

of

ilie Algebras

Thesis

Algebraic

C.

(

of

1.)

Group

specific approach Cohomology Theory

Work with

of

Theory

central extensions of groups

for

theory

finite

multiplier

/

simple

C.

2.) of

Subject Classification

(

3.)

D.

PROGRAMME

}

Homological Algebra

K

Homology Cohomology

cohomology group extensions of

Schur multiplier

central extensions

Projective

^Wednesdays

^of

^Group

specific ^approach Cohomology ^Theory

central extensions of _groups

2.) ^of

^Homology ^Cohomology

^cohomology ^group ^extensions ^of