- automorphisms of algebraic groups,
- maximum weight modules of algebraic groups,
- Steinberg endomorphisms,
- Lang-Steinberg theorem,
- tori and Sylow groups.
Finite Groups of Lie Type (M, 4.5 LP)
|Module Number||Module Name||CP (Effort)|
|MAT-43-21-M-7||Finite Groups of Lie Type||4.5 CP (135 h)|
|CP, Effort||4.5 CP = 135 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.
Finite Groups of Lie Type
|P||28 h||107 h||-||-||PL1||4.5||irreg.|
- About [MAT-43-21-K-7]: Title: "Finite Groups of Lie Type"; Presence-Time: 28 h; Self-Study: 107 h
Examination achievement PL1
- Form of examination: oral examination (20-30 Min.)
- Examination Frequency: irregular (by arrangement)
- Examination number: 86225 ("Finite Groups of Lie Type")
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 an in-depth knowledge of algebraic groups and know the groups of Lie type. They understand how statements about algebraic groups lead to a deeper understanding of these finite groups. They are able to name and to prove the essential propositions of the lecture as well as to classify and to explain the connections. They understand the proofs and are able to reproduce and explain them. In particular, they can critically assess, what conditions are necessary for the validity of the statements.
- R. Carter: Finite Groups of Lie Type, Conjugacy Classes and Complex Characters,
- F. Digne , J. Michel: Representations of Finite Groups of Lie Type,
- G. Malle, D. Testermann: Linear Algebraic Groups and Finite Groups of Lie Type.
Requirements for attendance (informal)
Additional knowledge from the module [MAT-40-25-M-4] is useful but not necessarily required.
- [MAT-10-1-M-2] Fundamentals of Mathematics (M, 28.0 LP)
- [MAT-43-20-M-7] Algebraic Groups (M, 9.0 LP)
Requirements for attendance (formal)