Module Handbook

• Dynamischer Default-Fachbereich geändert auf MAT

Module MAT-40-25-M-4

Module Identification

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

Basedata

CP, Effort 4.5 CP = 135 h 1 Sem. irreg. SuSe [4] Bachelor (Specialization) [EN] English Malle, Gunter, Prof. Dr. (PROF | DEPT: MAT) Fieker, Claus, Prof. Dr. (PROF | DEPT: MAT) Malle, Gunter, Prof. Dr. (PROF | DEPT: MAT) [MAT-AGCA] Algebra, Geometry and Computer Algebra [MAT-88.105-SG] M.Sc. Mathematics [NORM] Active

Notice

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

Courses

Type/SWS Course Number Title Choice in
Module-Part
Presence-Time /
Self-Study
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
U-Schein
- 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")

Contents

• 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.

Literature

• 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

Registration for the exercise classes via the online administration system URM (https://urm.mathematik.uni-kl.de)

None

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

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