Quotient Groups and Homomorphisms

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Related lectures (32)

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Group Theory Basics: Subgroups and Homomorphisms

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

Group Theory Basics

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

Automorphism Groups: Trees and Graphs III

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

Group Actions: Examples and Applications

Explores examples of group actions on sets, emphasizing the utility of group actions to understand groups.

Group Theory: Quotients of Group

Covers normal subgroups, quotient groups, homomorphisms, and the categorical viewpoint in group theory.

Groups: Definitions, Properties, and Homomorphisms

Introduces the basic concepts of groups, including definitions, properties, and homomorphisms, with a focus on subgroup properties and normal subgroups.

Push-out and Quotients

Delves into push-out and quotients in group theory, emphasizing homomorphisms and normal subgroups.

Recap of Group Theory

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

Symmetric Group: Cycle Notation

Explores the symmetric group, emphasizing cycle notation and group properties.

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.