250057 VO Group theory (2021S)

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 gives an introduction to modern group theory, covering the usual material, ranging from subgroups, quotients, homomorphisms, semidirect products, automorphisms, extensions and Sylow theorems, to solvable and nilpotent groups,
linear groups, free groups, presentation of groups by generators and relations, free products, classical groups and representations of finite groups.