Group Theory: Free Abelian Groups

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

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

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

Explores the concept of torsion in group theory, focusing on its Hom functoriality and its role in exact sequences.

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