Universität Wien
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250057 VO Group theory (2021S)

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

The course will take place on zoom. The room is: 974 9324 6659
Ask the teacher for the password.

  • Wednesday 03.03. 11:30 - 13:45 Digital
    Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 10.03. 11:30 - 13:45 Digital
    Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 17.03. 11:30 - 13:45 Digital
    Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 24.03. 11:30 - 13:45 Digital
    Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 14.04. 11:30 - 13:45 Digital
    Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 21.04. 11:30 - 13:45 Digital
    Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 28.04. 11:30 - 13:45 Digital
    Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 05.05. 11:30 - 13:45 Digital
    Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 12.05. 11:30 - 13:45 Digital
    Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 19.05. 11:30 - 13:45 Digital
    Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 26.05. 11:30 - 13:45 Digital
    Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 02.06. 11:30 - 13:45 Digital
    Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 09.06. 11:30 - 13:45 Digital
    Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 16.06. 11:30 - 13:45 Digital
    Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 23.06. 11:30 - 13:45 Digital
    Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 30.06. 11:30 - 13:45 Digital
    Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock

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 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: Fr 12.05.2023 00:21