Lectures related to Group Direct Sums in Group Theory

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

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

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

Delves into direct sums of abelian groups, showcasing their coproduct properties and universal verification.

Demonstrates the existence of direct sums of abelian groups and covers propositions and proofs related to their uniqueness.

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

Covers direct sums of abelian groups, group actions, and vector spaces, including coproducts and homomorphisms.

Explores the arithmetic of direct sums in group theory, discussing conditions for equality.

Explores the arithmetic of direct sum of abelian groups and the process of turning a monoid into a commutative group.