Permutation groups
Lecture: Thursday 14:00–15:30 in K334KA.
What we did
| date | content | |
|---|---|---|
| 19.02. | No lecture. | |
| 26.02. | Plan: some motivating examples. | |
| 05.03. | ||
| 12.03. | ||
| 19.03. | ||
| 26.03. | ||
| 02.04. | ||
| 09.04. | ||
| 16.04. | ||
| 23.04. | ||
| 30.04. | ||
| 07.05. | ||
| 14.05. | ||
| 21.05. |
Recommended literature
Permutation groups
- John D. Dixon, Brian Mortimer: Permutation Groups. This is one of the main sources for the course. It contains the full proof of O’Nan–Scott theorem.
- Peter Cameron: Permutation Groups. This is the second main source for the course, maybe slightly more readable. It has only the statement of O’Nan–Scott theorem and several applications.
- Helmut Wielandt: Finite Permutation Groups. A bit older book, but very readable, probably the first book on permutation groups.
Group theory
- Joseph J. Rotman: An Introduction to the Theory of Groups. In my opinion the best book on group theory, covers also a bit of permutation groups.
- Nathan Carter: Visual Group Theory. The content of this book is elementary, but the exposition is unique. The author explains the basic concepts of group theory via Cayley graphs. Highly recommended even for experts.
Groups and geometry
- Peter M. Neumann, Gabrielle A. Stoy, Edward C Thompson: Groups and Geometry. The first half of the book covers basics of (permutation) groups and the second half of the book is an introduction to geometry in the sense of Klein.
- Alexei B. Sosinski: Geometries. A very nice and modern exposition of many different types of geometries, where Klein’s Erlangen Program (the action of transformation groups) is systematically used as a basis for defining various geometries.
- Vaughn Climenhaga, Anatole Katok: From Groups to Geometry and Back. This book explores connections between group theory and geometry, introducing some of the main ideas of transformation groups, algebraic topology, and geometric group theory.
Groups and graphs
- Chris Godsil, Gordon Royle: Algebraic Graph Theory. The first half of the book focuses on groups of automorphisms of graphs.
- Ted Dobson, Aleksander Malnič, Dragan Marušič: Symmetry in Graphs. The book focuses on the study of highly symmetric graphs, particularly vertex-transitive graphs, and other combinatorial structures, primarily by group-theoretic techniques.
Additional problems
- John J. Dixon: Problems in Group Theory. A nice book of problems. You can try to prove various results from the 50s and 60s by yourself. It contains also hints and solutions to all problems.