# 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:

- Basic notions, the Lagrange theorem, isomorphism theorems
- Groups acting on sets, the Cayley's theorem, the Burnside's theorem
- The Sylow's theorem(s)
- Solvable groups
- Nilpotent groups
- Products
- Simple groups

Here are materials provided at the tutorial:
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### Literature

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