Universal Property of Groups

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Related lectures (30)

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Group Homomorphisms

Explores group homomorphisms, constructing isomorphisms between groups using generators and relations.

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Isomorphism Theorems: Third Isomorphism Theorem

Explores the third isomorphism theorem in group theory, focusing on quotient groups and a categorical perspective.

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.

Cohomology: Cross Product

Explores cohomology and the cross product, demonstrating its application in group actions like conjugation.

Topology: Free Groups and Their Properties

Discusses the theory of free groups, their properties, and relationships with other algebraic structures.

Recap of Group Theory

Provides a recap of group theory, defining a group as a set with a multiplication operation.

Local structure of totally disconnected locally compact groups III

Explores the local structure of totally disconnected locally compact groups and their isomorphisms through conjugation.

Homology of Riemann Surfaces

Explores the homology of Riemann surfaces, including singular homology and the standard n-simplex.

Group Homomorphisms

Explores group homomorphisms, Euler's phi function, and group products.