Daniil Rudenko
Group theory, Autumn 2020 (video lectures)
1.1: Symmetries.
1.2: Definition of a group.
1.3: Corollaries of the axioms.
1.4: Examples.
1.5: Orders, subgroups, isomorphism.
1.6: Lagrange Theorem.
1.7: Some history and the plan of the course.
2.1: Equivalence relations.
2.2: Cyclic structure of a permutation.
2.3: Generators of the symmetric group.
2.4: Conjugation in the symmetric group.
2.5: Homomorphisms.
2.6: Cayley theorem.
2.7: Sign (I).
2.8: Sign (II).
3.1: Cosets.
3.2: Index, Lagrange theorem.
3.3: Normal subgroups.
3.4: Normal subgroups of S4.
3.5: Quotient group.
3.6: First Homomorphism Theorem.
3.7: Lattice of subgroups.
3.8: Correspondence Theorem.
4.1: Cyclic groups.
4.2: Euler function.
4.3: Properties of Euler function.
4.4: Abelian groups.
4.5: Quadratic residues.
5.1: Group actions.
5.2: Orbits and Stabilizers.
5.3: Projective Space (I).
5.4: Projective Space (II).
6.1: First Sylow Theorem.
6.1: Second Sylow Theorem.