Lectures related to Introduction to Group Theory

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

Focuses on demonstrating properties using Lemma 3.4 in group theory.

Covers group actions, conjugacy classes, centralizers, direct products, and finite abelian groups.

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

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

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

Explores group operations with cyclic properties and the universal ownership of quotients.

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

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