Úvod do teorie grup

Introduction to Group Theory
Winter semester 2022/2023

1. Basic properties of groups
* Lagrange theorem
* Isomorphism theorems
2. Groups acting on sets
* Burnsides lemma
* Class formula
* p-groups
3. Sylow§s theorem(s)
4. Solvable groups
* Jordan-Hölder's theorem, Schreier's theorem
* Solvable grous and their properties
5. Nilpotent groups
6. Products
* Direct product of groups
* Semidirect product
* Wreath product (not at the exam)
7. Finite simple groups
* Alternating groups
* Special linear groups