Universität Wien

250057 VO Group theory (2023S)

5.00 ECTS (3.00 SWS), SPL 25 - Mathematik

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Details

Language: English

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

  • Wednesday 01.03. 11:30 - 13:00 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Wednesday 08.03. 11:30 - 13:00 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Wednesday 15.03. 11:30 - 13:00 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Monday 20.03. 09:45 - 10:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Wednesday 22.03. 11:30 - 13:00 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Monday 27.03. 09:45 - 10:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Wednesday 29.03. 11:30 - 13:00 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Monday 17.04. 09:45 - 10:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Wednesday 19.04. 11:30 - 13:00 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Monday 24.04. 09:45 - 10:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Wednesday 26.04. 11:30 - 13:00 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Wednesday 03.05. 11:30 - 13:00 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Monday 08.05. 09:45 - 10:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Wednesday 10.05. 11:30 - 13:00 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Monday 15.05. 09:45 - 10:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Wednesday 17.05. 11:30 - 13:00 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Monday 22.05. 09:45 - 10:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Wednesday 24.05. 11:30 - 13:00 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Wednesday 31.05. 11:30 - 13:00 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Monday 05.06. 09:45 - 10:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Wednesday 07.06. 11:30 - 13:00 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Wednesday 14.06. 11:30 - 13:00 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Monday 19.06. 09:45 - 10:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Wednesday 21.06. 11:30 - 13:00 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Monday 26.06. 09:00 - 10:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß

Information

Aims, contents and method of the course

Groups arise in the context of symmetries of all kinds. A systematic study was originally motivated by the classification of crystals (Schönflies, Fedorov), by solving algebraic equations (Galois), by solving differential equations (Lie), and by studying representations (Frobenius).

This lecture course will give an introduction to modern group theory, concentrating on finite groups. We will start with the axiomatics, and basic notions such as subgroups, quotients, homomorphisms. We will then move on to discuss semidirect products, automorphisms, group actions, extensions, Sylow theorems, solvable and nilpotent groups, free groups, presentations of groups by generators and relations, free products, and groups arising in Euclidean geometry.

Assessment and permitted materials

Written or oral examination.

Minimum requirements and assessment criteria

Useful prerequisites include abstract Linear algebra and Algebra courses, though everything will be developed from first principles. Both the written and the oral exams will contain a mixture of recollection of material taught, and problems that the students need to solve.

Examination topics

All topics covered in the lecture course.

Reading list

[ART] Michael Artin, Algebra, 2nd edition, Chapters 2, 6 and 7
[SER] Jean-Pierre Serre, Finite groups, an introduction. I.
[BOG] Bogopolski, O. Introduction to group theory. European Mathematical Society (EMS), Zürich, 2008.
[BUR] Burde, D. Lecture Notes on Group Theory. Vienna 2017.
[HUP] Huppert, B. Finite Groups. Band 134, Springer-Verlag, 1967.
[ROB] Robinson, Derek J. S., A Course in the Theory of Groups, Springer-Verlag, 1995.
[ROT] Rotman, Joseph J, An introduction to the theory of groups. Springer-Verlag, 1995.
[ZAS] Zassenhaus, Hans J. The theory of groups. Reprint of the 1958 edition, Dover Publications 1999.

Association in the course directory

MALG

Last modified: Mo 04.03.2024 14:26