Direct Sums: Abelian Groups

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Group Theory - Part 2

Explores Cayley tables, group operations, homomorphisms, Lie groups, and differentiable groups.

Group Theory: Direct Sum of Abelian Groups

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

Group Theory: Free Abelian Groups

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

Concrete Categories

Covers concrete categories with sets and structures, including Ens, Gr, Ab, and Vectk.

Direct Sum Construction

Covers the existence and uniqueness of direct sums in abelian groups.

Homomorphism of Groups: Signature

Explores homomorphisms of groups, focusing on the signature sgn and the concept of cycles and transpositions.

Group Actions: Theory and Examples

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

Quotients in Abelian Groups

Covers quotients in abelian groups and the concept of free abelian groups, showing that every abelian group is isomorphic to a quotient of a free abelian group.

Direct Sum of Abelian Groups

Explores the direct sum of abelian groups, emphasizing bijections and uniqueness.

Exact Sequences: Torsion and Divisibility

Explores exact sequences of abelian group homomorphisms and provides examples.