Homomorphisms and Isomorphisms of Groups

Chapter knowledge map

Learning structure

See the chapter's sections and source-backed lessons as an ordered visual learning path before choosing where to begin.

Interactive concept atlas

Homomorphisms and Isomorphisms of Groups Learning Map

25 concepts · 24 relationships · auto mode

Concept map ready to load

The graph engine loads only when this learning map approaches the viewport.

Accessible text outline

Concepts

Homomorphisms and Isomorphisms of Groupschapter
Homomorphisms of Groupssection
Homomorphism of Groupssubsection
Basic Properties of Homomorphismssubsection
Kernel of a Homomorphismsubsection
Epimorphism, Monomorphism, Isomorphism, and Automorphismsubsection
Natural Homomorphismsubsection
Isomorphism Tests and Examplessubsection
Classification of Cyclic Groupssubsection
Homomorphisms Between Cyclic Groupssubsection
Power Maps on Groupssubsection
Cayley Theorem and Permutation Groupssubsection
Isomorphism and Correspondence Theoremssection
Factorization Through Quotientssubsection
First Isomorphism Theoremsubsection
Homomorphic Images and Normal Subgroupssubsection
Second Isomorphism Theoremsubsection
Third Isomorphism Theoremsubsection
Correspondence Theoremsubsection
Group Actionssection
Group Actions and G-Setssubsection
Orbits and Stabilizerssubsection
Orbit-Stabilizer Formula and Orbit Countingsubsection
Permutation Representations and Extended Cayley Theoremsubsection
Fixed Points and Burnside's Lemmasubsection

Relationships

Homomorphisms and Isomorphisms of Groups --contains--> Homomorphisms of Groups
Homomorphisms of Groups --contains--> Homomorphism of Groups
Homomorphisms of Groups --contains--> Basic Properties of Homomorphisms
Homomorphisms of Groups --contains--> Kernel of a Homomorphism
Homomorphisms of Groups --contains--> Epimorphism, Monomorphism, Isomorphism, and Automorphism
Homomorphisms of Groups --contains--> Natural Homomorphism
Homomorphisms of Groups --contains--> Isomorphism Tests and Examples
Homomorphisms of Groups --contains--> Classification of Cyclic Groups
Homomorphisms of Groups --contains--> Homomorphisms Between Cyclic Groups
Homomorphisms of Groups --contains--> Power Maps on Groups
Homomorphisms of Groups --contains--> Cayley Theorem and Permutation Groups
Homomorphisms and Isomorphisms of Groups --contains--> Isomorphism and Correspondence Theorems
Isomorphism and Correspondence Theorems --contains--> Factorization Through Quotients
Isomorphism and Correspondence Theorems --contains--> First Isomorphism Theorem
Isomorphism and Correspondence Theorems --contains--> Homomorphic Images and Normal Subgroups
Isomorphism and Correspondence Theorems --contains--> Second Isomorphism Theorem
Isomorphism and Correspondence Theorems --contains--> Third Isomorphism Theorem
Isomorphism and Correspondence Theorems --contains--> Correspondence Theorem
Homomorphisms and Isomorphisms of Groups --contains--> Group Actions
Group Actions --contains--> Group Actions and G-Sets
Group Actions --contains--> Orbits and Stabilizers
Group Actions --contains--> Orbit-Stabilizer Formula and Orbit Counting
Group Actions --contains--> Permutation Representations and Extended Cayley Theorem
Group Actions --contains--> Fixed Points and Burnside's Lemma

Learning structure

Homomorphisms and Isomorphisms of Groups Learning Map

Concepts

Relationships

Sections

Homomorphisms of Groups

Isomorphism and Correspondence Theorems

Group Actions

Curated pathways

Metric Spaces

Introduction To Discrete Mathematics