Module Handbook

  • Dynamischer Default-Fachbereich geändert auf MAT

Module MAT-43-21-M-7

Finite Groups of Lie Type (M, 4.5 LP)

Module Identification

Module Number Module Name CP (Effort)
MAT-43-21-M-7 Finite Groups of Lie Type 4.5 CP (135 h)

Basedata

CP, Effort 4.5 CP = 135 h
Position of the semester 1 Sem. irreg.
Level [7] Master (Advanced)
Language [EN] English
Module Manager
Lecturers
Area of study [MAT-AGCA] Algebra, Geometry and Computer Algebra
Reference course of study [MAT-88.105-SG] M.Sc. Mathematics
Livecycle-State [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.
2V MAT-43-21-K-7
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.


Contents

  • automorphisms of algebraic groups,
  • maximum weight modules of algebraic groups,
  • Steinberg endomorphisms,
  • Lang-Steinberg theorem,
  • tori and Sylow groups.

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.

Literature

  • 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.

Modules:

Courses

Requirements for attendance (formal)

None

References to Module / Module Number [MAT-43-21-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.)