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Pro-/Seminar on Algebra - Symmetries

  • FU-Students should register via Campus Management.
  • Non-FU-students should register via MyCampus/Whiteboard.

Summer Semester 2021

Lecturer:  Dr. Gabriel Angelini-Knoll

  • Time and place:  Wednesdays, 10:00-12:00 h, online

  • Criteria for proof of performance:  a presentation and written summary

Target group: Students in the 3rd semester of mathematics.
Requirements: Only knowledge of some basic mathematical terms (group, vector space, linear mapping, metric, scalar product) is assumed. In addition to learning mathematical content, the goal of a proseminar is also to gain first experiences with scientific presentations in front of an audience.

Content: Symmetry is a phenomenon that plays a role in all natural sciences. Groups and the term group operation were invented to describe symmetries of mathematical objects. In this proseminar we will first examine the symmetries of figures in the plane and develop the basic mathematical terms "group" and "group operation", which are needed to describe symmetries. Later lectures will deal with groups with amazing properties.


14.04. Introduction and
Talk 1: Symmetry Motivation
Gabriel Angelini-Knoll
21.04. Talk 2: Isometries of the plane Jasper Seidensticker
28.04. Talk 3: Classification of isometries of the plane Hannah Schleupner
05.05. Talk 4: Finite groups of motions of the plane Emma Linn Stingele
12.05. Talk 5: Discrete groups of motions of the plane, Part I Urs Degendorfer
  Talk 6: Discrete groups of motions of the plane, Part II Eliza Baumann
19.05. Talk 7: Group actions Sebastian Schneider
26.05. Talk 8: Group actions on cosets and counting formulas Tianyi Hu
02.06. Talk 9: Permutation representations Taha Rayan
  Talk 10: Finite subgroups of the rotation group Lea Sophie Dohle
09.06. Talk 11: Groups and Graphs Luc Schoenmakers
16.06. Talk 12: Cayley graphs Kai Schweda
23.06. Talk 13: Symmetries of Cayley graphs and fundamental domains Mark Backhaus
  Talk 14: Free groups and group presentations Gerrit Charlotte Guddorf
30.06. Talk 15: Free groups and graphs Yannic Pascal Wendt
07.07. Talk 16: Subgroups of free groups Linus Dickert
14.07. Talk 17: The group ℤ/ℤ3 ∗ ℤ/4ℤ Florian Streckenbach


  • M. A. Armstrong. Groups and Symmetry. Undergraduate Texts in Mathematics. 1988. 
  • Michael Artin. Algebra. Birkhäuser Verlag, Basel, 1993.
  • John Meier. Groups, graphs and trees. Cambridge University Press, Cambridge, 2008.
  • Oleg Bogopolski. Introduction to group theory. European Mathematical Society (EMS), Zü̈rich, 2008.