Classification of Finite Abelian Groups

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

Covers algorithms for big numbers, Z_n, and orders in a group, explaining arithmetic operations and cryptographic concepts.

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

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.

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

Presents the classification of finite abelian groups as products of cyclic groups, a fundamental result in various branches of mathematics.

Focuses on abelian p-groups, demonstrating technical results for classifying finite abelian groups.

Explores the study of finite groups through subgroup analysis, focusing on Sylow subgroups.