Group Actions: G-object Notion

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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.

Algebraic Structures of Morphism Spaces

Explores algebraic structures of morphism spaces, including stability properties and injective ring homomorphisms.

Group Theory: Group Actions on Products

Covers defining group actions on products and constructing automorphisms in group theory.

Automorphism groups: Trees and Graphs

Explores automorphism groups in trees and graphs, focusing on ends and types of automorphisms.

Group Homomorphisms

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

Group Actions on Sets

Explores group actions on sets through homomorphisms and Cartesian products, illustrating their properties and equivalent definitions.

Groups & Rings: Morphisms, Kernels, and Injectivity

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

Group Actions: Theory and Examples

Explores concrete examples of group actions on sets, focusing on actions that do not change the set.

Recap of Group Theory

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

Two Definitions of Group Action

Explores two definitions of group action on a set, focusing on properties and applications.