Lectures related to Torsion: Hom Functoriality and Exact Sequences

Group Theory: Free Abelian Groups

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

Group Presentations: Abelian Groups

Covers exact sequences, torsion, divisibility, and operations on abelian groups.

Sylow Subgroups: Structure and Properties

Explores the properties and structure of Sylow subgroups in group theory, emphasizing a theorem-independent approach.

Divisibility and Torsion

Explores divisibility and torsion in group theory, focusing on defining a functor that preserves divisibility.

Hom Functor: Abelian Groups

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

Group Actions: Equivariance and Functors

Explores equivariance in group actions and functors, demonstrating its importance in group theory.

The Lemma of the Five: Abelian Groups

Presents the Lemma of the Five, a fundamental result in group theory.

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.

Functor Hom: Abelian Groups

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

Group Theory: Torsion and Divisibility

Covers the concepts of torsion and divisibility in group theory.

Abelian Groups: Free Abelian Groups

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

Active Learning: Group Theory

Explores adjoint functors, points fixes, orbits, and non-trivial actions in group theory.

Torsion and Divisibility in Group Theory

Explores the relationship between p-torsion and p-divisibility in group theory, highlighting implications of p-divisibility in exact sequences of abelian groups.

Group Direct Sums in Group Theory

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

Free Abelian Groups: Group Theory

Explores the concept of free abelian groups as an important left adjoint functor.

Finitely Generated Abelian Groups

Explores finitely generated abelian groups, focusing on their structure and isomorphism theorems.

Resoluble Groups: Quotients of Group

Covers the definition of solvable groups and the abelian property of group quotients.

Sylow Subgroups: Group Theory

Explores the concept of p-subgroups of Sylow in group theory, emphasizing the philosophy of studying mathematical objects 'one prime at a time'.

Natural Transformations: Functors and Categories

Explores functors, natural transformations, and the theory of groups, emphasizing the importance of comparisons and structure preservation.

Torsion and Divisibility: Abelian Groups

Introduces torsion and divisibility concepts in abelian groups to describe their structure.