Lectures related to Torsion and Divisibility: Abelian Groups

Symmetry and Group Theory

Explores chirality, group completeness, Abelian groups, conjugate classes, and isomorphic groups in symmetry and group theory.

Untitled

Direct Sums Arithmetic

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

Abelian Groups: First Approach

Introduces the theory of abelian groups, focusing on p-abelian groups and their structure.

Groups: Definitions, Properties, and Homomorphisms

Introduces the basic concepts of groups, including definitions, properties, and homomorphisms, with a focus on subgroup properties and normal subgroups.

Resoluble Groups: Quotients of Group

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

Applications of Lagrange's Theorem

Explores the applications of Lagrange's theorem in algebra, covering corollaries, cyclic groups, and quotient groups.

Finitely Generated Abelian Groups

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

Torsion: Hom Functoriality and Exact Sequences

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

Groups and Numbers: Mathematical Elements on Groups

Explores fundamental properties of groups and numbers, emphasizing equivalence classes and subgroup concepts.

Existence of Sylow Subgroups: Proof by Recurrence

Demonstrates the existence of p-Sylow subgroups in any finite group using induction and the abelian case.

Sylow Subgroups: Structure and Properties

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

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'.

Introduction to Group Theory

Covers active learning, video lectures, exercises, categories, group actions, and abelian groups.

Divisibility and Torsion

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

Group Theory Basics: Subgroups and Homomorphisms

Introduces subgroups and homomorphisms in group theory, with examples for illustration.

Existence of Direct Sums: Abelian Groups

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

A Tool for Demonstrating Properties: Lemme 3.4

Focuses on demonstrating properties using Lemma 3.4 in group theory.

Useful Variants on Beta Action

Covers abelian groups, Sylow subgroups, and variants on beta action.

Categorical Perspective: Abelian Groups

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