Abelian p-groups: Groupes abéliens

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Covers useful lemmas for p-groups, including divisibility properties and the existence of specific elements in finite abelian groups.

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.

Group Presentations: Abelian Groups

Covers exact sequences, torsion, divisibility, and operations on abelian groups.

Symmetry and Group Theory

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

Finitely Generated Abelian Groups

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

Applications of Lagrange's Theorem

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

Categorical Perspective: Abelian Groups

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

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.

Torsion and Divisibility in Group Theory

Explores the relationship between p-torsion and p-divisibility in group theory, highlighting implications of p-divisibility in exact sequences of abelian groups.