Module Handbook

  • Dynamischer Default-Fachbereich geändert auf MAT

Module MAT-40-25-M-4

Character Theory of Finite Groups (M, 4.5 LP)

Module Identification

Module Number Module Name CP (Effort)
MAT-40-25-M-4 Character Theory of Finite Groups 4.5 CP (135 h)


CP, Effort 4.5 CP = 135 h
Position of the semester 1 Sem. irreg. SuSe
Level [4] Bachelor (Specialization)
Language [EN] English
Module Manager
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


Without a proof of successful participation in the exercise classes, only 3 credit points will be awarded for the module.


Type/SWS Course Number Title Choice in
Presence-Time /
SL SL is
required for exa.
PL CP Sem.
2V+1U MAT-40-25-K-4
Character Theory of Finite Groups
P 42 h 93 h
- PL1 4.5 irreg. SuSe
  • About [MAT-40-25-K-4]: Title: "Character Theory of Finite Groups"; Presence-Time: 42 h; Self-Study: 93 h
  • About [MAT-40-25-K-4]: The study achievement [U-Schein] proof of successful participation in the exercise classes (ungraded) must be obtained.

Examination achievement PL1

  • Form of examination: oral examination (20-30 Min.)
  • Examination Frequency: each semester
  • Examination number: 84139 ("Character Theory of Finite Groups")

Evaluation of grades

The grade of the module examination is also the module grade.


  • Maschke's theorem,
  • character tables,
  • orthogonality relations,
  • rationality questions,
  • Burnside theorem,
  • induced characters,
  • Frobenius groups.

Competencies / intended learning achievements

Upon successful completion of this module, the students have studied the basic terms, propositions and techniques of representation theory through the character theory of finite groups. In particular, they have learnt to work with generic characters and character tables. They are able to name and to prove the essential statements of the lecture as well as to classify and to explain the connections.

By completing the given exercises, the students have developed a skilled, precise and independent handling of the terms, propositions and techniques taught in the lecture. In addition, they have learnt how to apply these techniques to new problems, analyze them and develop solution strategies independently or by team work.


  • M. Isaacs: Character Theory of Finite Groups,
  • G. James, M. Liebeck: Representations and Characters of Finite Groups,
  • J. Alperin, R. Bell: Groups and Representations.


Registration for the exercise classes via the online administration system URM (

References to Module / Module Number [MAT-40-25-M-4]

Course of Study Section Choice/Obligation
[MAT-88.105-SG] M.Sc. Mathematics Pure Mathematics [WP] Compulsory Elective
[MAT-88.706-SG] M.Sc. Mathematics International Pure Mathematics [WP] Compulsory Elective
Module-Pool Name
[MAT-GM-MPOOL-5] General Mathematics (Introductory Modules M.Sc.)