Exercise Sheets
The exercise sheets will usually be uploaded here on Fridays and are due the second Monday after at 2pm. They should be submitted in mailbox no. 41. In the (exceptional) case that things prevent you from submitting via mailbox, you can send them by e-mail to Robin Lahni.
Sheet 13 (Due on 06/02/2023)
Exercises on Galois extensions.
Sheet 12 (Due on 30/01/2023)
Exercises on finite fields, separable and algebraic field extensions, splitting fields, and constructions with straight-edge and compass.
Sheet 11 (Due on 24/01/2023)
Exercises on Irreducibility and Möbius Inversion.
Sheet 10 (Due on 18/01/2023)
Reading exercise and questions about the classification of finite fields. The reading materials can be found here.
Sheet 9 (Due on 10/01/2023)
Representations of the symmetric group. The text by Zhao can be downloaded in the materials section here.
Sheet 8 (Due on 04/01/2023)
Exercises on the complex group ring and (representations of) SU(2). Please submit this sheet via e-mail.
Sheet 7 (Due on 21/12/2022)
Exercises on Schur's Lemma and induced/restricted representations, in particular the Frobenius reciprocity.
A number of solutions to the exercises can be found here.
Sheet 6 (Due on 12/12/2022)
Irreducible representations and representations of transitive actions.
Sheet 5 (Due on 05/12/2022)
Exercises on presentations and re(!)presentations of groups.
Sheet 4.5
Exercises to practice application of the Sylow Theorems. Not to be submitted.
Sheet 4 (Due on 28/11/2022)
Proofs of the Sylow Theorems
Sheet 3 (Due on 21/11/2022)
Topics are group actions, the quaternion group, and groups of order p3.
Sheet 2 (Due on 14/11/2022)
Sheet concerning discrete subgroups of groups of isometries and group actions of such groups.
Sheet 1 (Due on 07/11/2022)
First sheet to be submitted. Concerns isometries of the plane and Dihedral groups.
Sheet 0
This sheet is only for self preparation and will not be handed in. However, you are strongly advised to do the reading exercise.