Lectures related to Free Product: Group Theory

Explores group homomorphisms, Euler's phi function, and group products.

Explores the Hom functor for abelian groups and its relation to direct sums.

Discusses the theory of free groups, their properties, and relationships with other algebraic structures.

Explores the concept of direct sums in abelian groups, emphasizing the universal property and homomorphisms.

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

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

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

Covers the concept of group cohomology, focusing on chain complexes, cochain complexes, cup products, and group rings.

Explores the classification of extensions in group theory, emphasizing split extensions and semi-direct products.

Covers the concept of amalgams, defining pushouts and quotient groups in group theory.