Finitely generated abelian group

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Related lectures (31)

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Relation between Direct Sum and Hom

Explores the isomorphism between Hom(A, B) and Hom(A, B) for any abelian group B.

Uniqueness in Abelian Groups

Explores the uniqueness in abelian groups, emphasizing the structure and choices within the groups.

Abelian Groups: Technical Lemmas

Covers technical lemmas on abelian p-groups and maximal order elements.

Classification of Finite Abelian Groups

Covers the classification of finite abelian groups and the unique sequence of positive integers for isomorphism.

Existence in Abelian Case and Group Center

Explores the existence of p-Sylow subgroups in finite groups and the abelian group center.

Endomorphisms and automorphisms of totally disconnected locally compact groups

Explores endomorphisms and automorphisms of totally disconnected locally compact groups, emphasizing the properties of flat groups and free abelian subgroups.

Module Theory: Noetherian Modules

Introduces Noetherian modules and explores simple modules and composition series.

Sheaves: Hartshorne I.1

Covers the concept of sheaves, emphasizing the unique determination of functions by local data and the importance of direct limits.

Existence: Proof of Classification Theorem

Covers the proof of the Classification Theorem for finite abelian groups, demonstrating the existence of a decomposition into cyclic 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.