## Module Handbook

• Dynamischer Default-Fachbereich geändert auf MAT

# Module MAT-43-24-M-7

## Module Identification

Module Number Module Name CP (Effort)
MAT-43-24-M-7 Cohomology of Groups 9.0 CP (270 h)

## Basedata

CP, Effort 9.0 CP = 270 h 1 Sem. irreg. [7] Master (Advanced) [EN] English Lassueur, Caroline, Jun. Prof. Dr. (PROF | DEPT: MAT) Malle, Gunter, Prof. Dr. (PROF | DEPT: MAT) Fieker, Claus, Prof. Dr. (PROF | DEPT: MAT) Lassueur, Caroline, Jun. Prof. Dr. (PROF | DEPT: MAT) Malle, Gunter, Prof. Dr. (PROF | DEPT: MAT) Thiel, Ulrich, Prof. Dr. (PROF | DEPT: MAT) [MAT-AGCA] Algebra, Geometry and Computer Algebra [MAT-88.105-SG] M.Sc. Mathematics [NORM] Active

## Courses

Type/SWS Course Number Title Choice in
Module-Part
Presence-Time /
Self-Study
SL SL is
required for exa.
PL CP Sem.
4V MAT-43-24-K-7
Cohomology of Groups
P 56 h 214 h - - PL1 9.0 irreg.
• About [MAT-43-24-K-7]: Title: "Cohomology of Groups"; Presence-Time: 56 h; Self-Study: 214 h

## Examination achievement PL1

• Form of examination: oral examination (20-30 Min.)
• Examination Frequency: irregular (by arrangement)
• Examination number: 86156 ("Cohomology of Groups")

## Contents

• Semi-direct products,
• homological algebra,
• free, projective and injective resolutions,
• homology and cohomology of groups,
• group extensions and cohomology,
• Schur multiplier,
• central extensions,
• projective representations.

## Competencies / intended learning achievements

Upon successful completion of this module, the students have studied and understand the basic methods and statements of homology and cohomology of groups. They have learnt important examples and are able to investigate them by using scientific methods. They are able to name the essential propositions of the lecture as well as to classify and to explain the connections. They understand the proofs presented in the lecture and are able to comprehend and explain them. In particular, they are able to outline the conditions and assumptions that are necessary for the validity of the statements.

By completing exercises, the students have developed a skilled, precise and independent handling of the terms, propositions and techniques taught in the lecture.

## Literature

• K. Brown: Cohomology of Groups,
• C. Curtis & I. Reiner: Methods of representation theory with applications to finite groups and orders, vol. 1,
• J. Rotmann: An Introduction to the Theory of Groups,
• C. Weibel: An Introduction to Homological Algebra.

None

## References to Module / Module Number [MAT-43-24-M-7]

Module-Pool Name
[MAT-43-MPOOL-7] Specialisation Algebra and Number Theory (M.Sc.)
[MAT-RM-MPOOL-7] Pure Mathematics (Advanced Modules M.Sc.)