Introduction to the Theory of Groups

Exam: You will get three questions:

• A full topic (eg. Solvable groups) -- you will be supposed to provide an overview
• A theorem or a part of a topic (eg. The second isomorphism theorem) -- you will be asked for all details
• A problem to solve -- this is to test understanding and ability to apply the theory

Here is an example of an exam

Materials

Here you can download my (handwritten) lecture notes:

1. Basic notions, the Lagrange theorem, isomorphism theorems
2. Groups acting on sets, the Cayley's theorem, the Burnside's theorem
3. The Sylow's theorem(s)
4. Solvable groups
5. Nilpotent groups
6. Products
7. Simple groups

Here are materials provided at the tutorial: 1., 2., 3., 4., 5., 6., 7., 8., 9., 10., 11., 12.

Literature

1. Joseph J. Rotman, An Introduction to the Theory of Groups (4th ed.), Springer New York, NY, 2014.
2. Oleg Bogopolski, Introduction to Group Theory, European Mathematical Society, 2008.