First Isomorphism Theorem

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Uniqueness of Amalgams

Explores the uniqueness of amalgams in group theory through examples and diagrams.

Groups & Rings: Morphisms, Kernels, and Injectivity

Explores group morphisms, kernels, and injectivity in group theory.

Pushouts in Group Theory: Universal Properties Explained

Covers the construction and universal properties of pushouts in group theory.

Group Homomorphisms

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

Linear Applications: Definitions and Properties

Explores the definition and properties of linear applications, focusing on injectivity, surjectivity, kernel, and image, with a specific emphasis on matrices.

Push-out and Quotients

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

Universal Property of Groups

Explores the universal property of groups, defining homomorphisms and exploring subgroup properties.

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.

Abelian Groups: Free Abelian Groups

Explores free abelian groups, homomorphisms, and exact sequences in group theory.

Group Homomorphisms

Explores group homomorphisms, isomorphisms, and generators in abstract algebra.