- 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.
Cohomology of Groups (M, 9.0 LP)
|Module Number||Module Name||CP (Effort)|
|MAT-43-24-M-7||Cohomology of Groups||9.0 CP (270 h)|
|CP, Effort||9.0 CP = 270 h|
|Position of the semester||1 Sem. irreg.|
|Level|| Master (Advanced)|
|Area of study||[MAT-AGCA] Algebra, Geometry and Computer Algebra|
|Reference course of study||[MAT-88.105-SG] M.Sc. Mathematics|
|Type/SWS||Course Number||Title||Choice in |
|SL||SL is |
required for exa.
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")
Evaluation of grades
The grade of the module examination is also the module grade.
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.
- 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.
Requirements for attendance (informal)
- [MAT-12-11-K-2] Algebraic Structures (2V+2U, 5.5 LP)
- [MAT-12-22-K-3] Introduction to Algebra (2V+1U, 4.5 LP)
Requirements for attendance (formal)