Category of abelian groups

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Group Direct Sums in Group Theory

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

Endomorphisms and automorphisms of totally disconnected locally compact groups V

Explores endomorphisms and automorphisms of totally disconnected locally compact groups, emphasizing surjective homomorphisms and free abelian groups.

Functor Hom: Abelian Groups

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

Existence of Direct Sums: Abelian Groups

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

Exact Sequences: Torsion and Divisibility

Explores exact sequences of abelian group homomorphisms and provides examples.

Resoluble Groups: Quotients of Group

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

The Lemma of the Five: Abelian Groups

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

Finitely Generated Abelian Groups

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

Introduction to Group Theory

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

Direct Sum of Abelian Groups

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