Group Homomorphisms

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Related lectures (31)

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Automorphism Groups: Trees and Graphs III

Explores automorphism groups of trees and graphs, including actions on trees and group homomorphisms.

Group Theory Basics: Subgroups and Homomorphisms

Introduces subgroups and homomorphisms in group theory, with examples for illustration.

Dihedral Group: Symmetries and Cosets

Explores the symmetries of a regular n-gon, normal subgroups, cosets, and Lagrange's theorem.

Isomorphism Theorems: Third Isomorphism Theorem

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

Topology: Free Groups and Their Properties

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

Group Theory Basics

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

Normal Subgroups and Quotients

Introduces normal subgroups, group quotients, and their applications in group theory.

Active Learning: Group Homomorphisms

Explores group homomorphisms, emphasizing surjective mappings and their impact on group questions.

Categorical Perspective: Group Quotients

Explores the categorical sense of constructing a group quotient by a normal subgroup, showing it as a specific example of a more general construction.

Abelianization of Fundamental Group

Explores abelianization examples, homomorphisms, and isomorphisms in group theory.