Free Groups: Introduction and Examples

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Related lectures (30)

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Free Abelian Groups: Group Theory

Explores the concept of free abelian groups as an important left adjoint functor.

Endomorphisms and automorphisms of totally disconnected locally compact groups V

Explores endomorphisms and automorphisms of totally disconnected locally compact groups, emphasizing surjective homomorphisms and free abelian groups.

Combinatorial Group Theory

Introduces combinatorial group theory, emphasizing group presentations, normal subgroups, and group quotients.

Group Operations and Quotients

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

Invariant Definitions

Explores invariant definitions in sets, groups, and automorphisms, including p-divisible groups and free abelian groups.

Group Presentations: Abelian Groups

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

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Finite Abelian Groups & Rings

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

Resoluble Groups: Quotients of Group

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

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.