Lectures related to Class Equation and Burnside's Lemma

Explores direct sums in group theory, focusing on abelian groups and their implications.

Explores the universal property of groups, defining homomorphisms and exploring subgroup properties.

Explores the Hom functor in Abelian groups, focusing on its construction and properties.

Explores free abelian groups, homomorphisms, and exact sequences in group theory.

Explores direct products in group theory, including semi-direct products and group properties.

Covers the concept of morphism of groups, actions on sets, and automorphisms.

Explores abelian groups from a categorical perspective, discussing the coproduct construction.

Covers the adjoints of the restriction functor in group theory.

Covers the first isomorphism theorem in group theory and its applications.

Covers the verification of constructions in the context of abelian groups and Sylow subgroups.