Linked from

The 24 pages that link to Group homomorphism, each with the reason it gives.

• Group actionRelated: The action law makes the assignment from group elements to permutations a homomorphism.

• Group theoryRelated: Homomorphisms compare groups while preserving their algebraic structure.

• GroupRelated: Homomorphisms compare groups while retaining the structure of their operations.

• Complex exponentialRelated: The identity exp(z+w)=exp(z)exp(w) preserves addition as multiplication.

• Quotient groupRelated: A homomorphism’s kernel determines a quotient that captures its image.

• Group representationBroader topic: The defining map must preserve multiplication as composition of transformations.

• Normal subgroupRelated: The kernel of every group homomorphism is normal.

• Abelian groupRelated: Homomorphisms preserve the group structure used to compare Abelian groups.

• Orbit-stabilizer theoremRelated: The action can be encoded as a homomorphism from the group to a permutation group.

• Lagrange's theoremRelated: The first isomorphism theorem uses Lagrange’s theorem to relate kernel and image sizes.

• Alternating groupNarrower topic: The sign homomorphism identifies Aₙ as a kernel.

• Exact sequenceNarrower topic: Group homomorphisms provide a familiar setting for kernels, images, and exactness.

• Simple groupNarrower topic: Kernels of homomorphisms are normal subgroups, linking simplicity to possible group maps.

• Free groupRelated: A function on free generators determines a unique homomorphism from the free group.

• Burnside's lemmaRelated: An action can equivalently be represented by a homomorphism into a permutation group.

• Composition seriesRelated: Homomorphisms connect quotient groups to images and help analyze series.

• Cayley's theoremRelated: The left-multiplication assignment is a homomorphism because composing its permutations matches multiplication.

• MorphismBroader topic: Groups and their homomorphisms form a standard category.

• Pólya enumeration theoremRelated: The cycle-index substitution respects how permutation cycles act on color assignments.

• Snake lemmaRelated: Groups provide a familiar setting for the diagram and its induced maps.

• Five lemmaRelated: In abelian groups, the vertical maps can be group homomorphisms satisfying the lemma’s hypotheses.

• Isomorphism theoremsNarrower topic: The theorems describe how homomorphisms connect kernels, images, subgroups, and quotients.

• Zassenhaus lemmaRelated: Homomorphisms provide the general language behind the induced quotient isomorphisms.

• Fundamental theorem on homomorphismsNarrower topic: The theorem describes the structure preserved by this kind of map.