Classification of Finite Abelian Groups

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

Covers the Orbit-Stabilizer theorem, conjugacy classes, and direct products in finite groups.

Explores conjugation in groups, the direct product of groups, and the classification of finite abelian groups.

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

Explores Wedderburn's theorem, group algebras, and Maschke's theorem in the context of finite dimensional simple algebras and their endomorphisms.

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

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

Explores the classification of finite abelian groups and rings, emphasizing elementary divisors and properties of rings.

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