Character Theory of Finite Groups SS 2017


Lecture: Tuesdays 10:00-11:30 Room 48-438 Lecturer: Jun.-Prof. Dr. Caroline Lassueur
Exercises: Fridays 11:45 - 13:15 Room 48-438 Assistant: Dr. Inga Schwabrow
Office hour: Mondays 13:00-14:00 Lernzentrum, odd weeks, starting 24.04.17

Exam Dates:
  • 03.08.2017
  • 23.08.2017
  • 12.10.2017
  • 13.10.2017
  • 23.10.2017
Common dates with T. Hofmann are: 3.8., 23.8. und 23.10.
Please, register with Frau Sternike (Room 48-511).


The exercise classes begin in the 2nd week of the lecture period and then take place every second week. See [KIS] for the precise dates.

The 1st exercise sheet will be uploaded after the 1st lecture. From Sheet 2 on, the exercise sheets will be uploaded on the handing-in day of the previous one.

Exercise Sheet 1. Due date: 26.04.2017, 14:00
Exercise Sheet 2. Due date: 10.05.2017, 14:00
Exercise Sheet 3. Due Date: 24.05.2017, 14:00
Exercise Sheet 4. Due date: 07.06.2017, 14:00
Exercise Sheet 5. Due date: 21.06.2017, 14:00
Exercise Sheet 6. Due date: 05.07.2017, 14:00
Exercise Sheet 7. Due date: 19.07.2017, 14:00

Registration: Please register for the exercises in the URM system by Friday, the 21st of April 2017, noon.

Bei Fragen zu den Übungen stehen wir Ihnen gerne zur Verfügung.


You obtain an "Übungsschein" if the following criteria are fulfilled:
  • you have obtained minimum 50% of the points on the Exercise sheets altogether.
  • you have obtained minimum 1 point in 2 Exercises (out of 4) in each of the exercise sheets 1 to 7.
  • you have actively taken part to the exercise classes: attendance to the exercise classes + presenting at least one solution on the board.

Each Exercise is worth 4 points.
Exercises can be handed in in groups of maximum two students.


  • [JL01] G. James and M. Liebeck, Representations and characters of groups. See [zbMATH]
  • [Ser77] J.-P. Serre, Linear representations of finite groups. See [zbMATH]
    The original text is:
    [Ser98] J.-P. Serre, Représentations linéaires des groupes finis. See [zbMATH]
  • [Isa06] M. Isaacs, Character theory of finite groups. See [zbMATH]
  • [Web16] P. Webb, A course in finite group representation theory. See [zbMATH]
  • [CCNPW85] J.H. Conway, R.T. Curtis, S.P. Norton, R. Parker, R.A. Wilson, Atlas of Finite Groups. Clarendon Press, Oxford, 1985.

Oral Exam

In principle one should be able to explain the content of the lecture.
  • Definitions, statements of the theorems/propositions/lemmata should be known;
  • you should be able to explain short proofs as well as the red lines of the longer proofs;
  • the Exercises mentionend in the lecture are important for the understanding of the theory;
  • you should also be able to give concrete examples/counter-examples to illustrate the results;
  • there will also be questions on concrete examples.
  • Please, also be ready to write down formally the concepts and results you are explaining.

Contents of the Lecture

  • Linear representations and characters
  • Character tables, orthogonality relations
  • Burnside's \(p^aq^b\)-theorem
  • Restriction, induction, inflation, tensor products
  • Clifford theory
  • Brauer's characterisation of characters

Prerequisites: elementary group theory and linear algebra


Lecture : 2 SWS, i.e. 30 contact hours
Exercises : 1 SWS, i.e. 15 contact hours

Further Documents