Universität Wien
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250057 VO Group theory (2022S)

5.00 ECTS (3.00 SWS), SPL 25 - Mathematik
Moodle

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Details

Language: English

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

  • Tuesday 01.03. 09:45 - 12:00 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Tuesday 08.03. 09:45 - 12:00 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Tuesday 15.03. 09:45 - 12:00 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Tuesday 22.03. 09:45 - 12:00 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Tuesday 29.03. 09:45 - 12:00 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Tuesday 05.04. 09:45 - 12:00 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Tuesday 26.04. 09:45 - 12:00 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Tuesday 03.05. 09:45 - 12:00 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Tuesday 10.05. 09:45 - 12:00 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Tuesday 17.05. 09:45 - 12:00 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Tuesday 24.05. 09:45 - 12:00 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Tuesday 31.05. 09:45 - 12:00 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Tuesday 14.06. 09:45 - 12:00 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Tuesday 21.06. 09:45 - 12:00 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Tuesday 28.06. 09:45 - 12:00 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 gives an introduction to modern group theory, covering the usual material, ranging from subgroups, quotients, homomorphisms, semidirect products, automorphisms, extensions and Sylow theorems, to solvable and nilpotent groups,
linear groups, free groups, presentation of groups by generators and relations, free products, classical groups and –if time allows– representations of finite groups.

Assessment and permitted materials

Written or oral exam. In case that presence examination is not possible, written or oral online exam.

Minimum requirements and assessment criteria

Linear algebra I, II and abstract algebra I.

To pass the exam.

Examination topics

All topics covered in the lecture.

Reading list

[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 11.07.2022 12:29