Lectures related to Direct Products in Group Theory

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

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

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

Covers the goals and motivations of representation theory, focusing on associative algebras and homomorphisms.

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

Provides a recap of group theory, defining a group as a set with a multiplication operation.

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

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

Explores concrete examples of group actions on sets, focusing on actions that do not change the set.