Lectures related to Classification of Finite Abelian Groups

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.

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.