Universität Wien

250057 VO Group theory (2020S)

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

  • Monday 02.03. 15:00 - 15:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 03.03. 13:15 - 14:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 09.03. 15:00 - 15:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 10.03. 13:15 - 14:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 16.03. 15:00 - 15:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 17.03. 13:15 - 14:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 23.03. 15:00 - 15:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 24.03. 13:15 - 14:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 30.03. 15:00 - 15:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 31.03. 13:15 - 14:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 20.04. 15:00 - 15:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 21.04. 13:15 - 14:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 27.04. 15:00 - 15:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 28.04. 13:15 - 14:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 04.05. 15:00 - 15:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 05.05. 13:15 - 14:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 11.05. 15:00 - 15:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 12.05. 13:15 - 14:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 18.05. 15:00 - 15:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 19.05. 13:15 - 14:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 25.05. 15:00 - 15:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 26.05. 13:15 - 14:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 08.06. 15:00 - 15:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 09.06. 13:15 - 14:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 15.06. 15:00 - 15:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 16.06. 13:15 - 14:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 22.06. 15:00 - 15:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 23.06. 13:15 - 14:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 29.06. 15:00 - 15:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 30.06. 13:15 - 14:45 Seminarraum 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, and cohomology of groups.

Assessment and permitted materials

Take-home exam and Online-teaching: Please read the text for each week at the course page at my homepage required for the 3 exercises.

Minimum requirements and assessment criteria

Linear algebra I, II and abstract algebra I.

Examination topics

All topics covered in the lecture.

Reading list

[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: Tu 09.02.2021 17:30