Torsion and Divisibility: Abelian Groups

About
Privacy
Disclaimer

Graph Chatbot

Related lectures (31)

Page 3 of 4

Group Operations and Quotients

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

Abelian p-groups: Groupes abéliens

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

Group Presentations: Abelian Groups

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

Algebra: Practice Exam Solutions

Covers the solution of a practice exam in Algebra, focusing on finding greatest common divisors of polynomials and exploring group properties.

Subgroups and Cosets: Lagrange's Theorem

Explores subgroups, normal subgroups, cosets, and Lagrange's theorem in group theory, emphasizing the importance of left cosets.

Hom Functor: Abelian Groups

Explores the Hom functor for abelian groups and its relation to direct sums.

Direct Sums: Lemme 1.2

Delves into direct sums of abelian groups, showcasing their coproduct properties and universal verification.

Quotients in Abelian Groups

Covers quotients in abelian groups and the concept of free abelian groups, showing that every abelian group is isomorphic to a quotient of a free abelian group.

Group Theory Basics

Introduces the basics of group theory, covering definitions, examples, subgroups, and homomorphisms.

The Lemma of the Five: Abelian Groups

Presents the Lemma of the Five, a fundamental result in group theory.