4. Group theory - Lagrange's theorem, group action and Burnside's theorem, the structure of cyclic groups, homomorphisms, factorgroups, solvability 5.

Field extensions - dimension, ruler and compass constructions, splitting fields and finite fields 6. Galois theory - Galois groups, solving polynomial equations vs. field extensions vs. properties of Galois groups, Abel-Ruffini theorem

Introductory course for the second year students of mathematics.

Commutative algebra and field theory.