Concept

Elementary abelian group

Related lectures (31)

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

Finite Abelian Groups: Classification Theorem

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

Finite Abelian Groups & Rings

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

Classification of Finite Abelian Groups

Covers the classification theorem for finite abelian groups and introduces rings, including zero divisors and domains.

Group Presentations: Abelian Groups

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

Categorical Perspective: Abelian Groups

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

Finitely Generated Abelian Groups

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

Conjugation in Groups

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

Orbit-Stabilizer Theorem: Conjugacy Classes and Direct Products

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

Abelian Groups: Fourth Property

Explores the fourth property of p-Sylow subgroups in abelian groups.

Algebra Review: Rings, Fields, and Groups

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

Introduction to Group Theory

Covers active learning, video lectures, exercises, categories, group actions, and abelian groups.

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.

Abelian Groups: First Approach

Introduces the theory of abelian groups, focusing on p-abelian groups and their structure.

Symmetry and Group Theory

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

Group Theory - Part 2

Explores Cayley tables, group operations, homomorphisms, Lie groups, and differentiable groups.

Abelian Groups: Technical Lemmas

Covers technical lemmas on abelian p-groups and maximal order elements.

Group Operations and Quotients

Explores group operations with cyclic properties and the universal ownership of quotients.

Resoluble Groups: Quotients of Group

Covers the definition of solvable groups and the abelian property of group quotients.