Classification of Finite Abelian Groups

Related lectures (30)

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Covers the Chinese remainder theorem for commutative rings and integers, polynomial rings, and Euclidean domains.

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

Demonstrates the existence of p-Sylow subgroups in any finite group using induction and the abelian case.

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

Explores the properties and structure of Sylow subgroups in group theory, emphasizing a theorem-independent approach.

Explores operations on ideals and structure theorems in commutative rings.

Covers proper actions of groups on Riemann surfaces and introduces algebraic curves via square roots.

Covers a review of algebraic structures such as rings, fields, and groups, including integral domains, ideals, and finite fields.

Explores the arithmetic of direct sums in group theory, discussing conditions for equality.

Delves into group theory, emphasizing the centralizer of elements and the classification of finite abelian groups.