250057 VO Group theory (2023S)

Groups arise in the context of symmetries of all kinds. A systematic study was originally motivated by the classification of crystals (Schönflies, Fedorov), by solving algebraic equations (Galois), by solving differential equations (Lie), and by studying representations (Frobenius).

This lecture course will give an introduction to modern group theory, concentrating on finite groups. We will start with the axiomatics, and basic notions such as subgroups, quotients, homomorphisms. We will then move on to discuss semidirect products, automorphisms, group actions, extensions, Sylow theorems, solvable and nilpotent groups, free groups, presentations of groups by generators and relations, free products, and groups arising in Euclidean geometry.