Finitely Generated Abelian Groups

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Isomorphism: Order of Group Elements

Explores isomorphism and the order of group elements, emphasizing matching identities and inverses.

Direct Sums: Lemme 1.2

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

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.

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.

Group Operations and Quotients

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

Torsion and Divisibility: Abelian Groups

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

Useful Variants on Beta Action

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

Isomorphism Theorems: Third Isomorphism Theorem

Explores the third isomorphism theorem in group theory, focusing on quotient groups and a categorical perspective.

Group Direct Sums in Group Theory

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