Linked from

The 18 pages that link to Normal subgroup, each with the reason it gives.

• Congruence relationRelated: Normal subgroups correspond exactly to congruences on groups.

• Group homomorphismRelated: Every group homomorphism's kernel is a normal subgroup.

• CosetRelated: A subgroup is normal exactly when all its left and right cosets coincide.

• Conjugacy classRelated: A subgroup is normal exactly when it is a union of conjugacy classes.

• Finite simple groupRelated: Normality is the exact condition used to define simplicity.

• Jordan–Hölder theoremRelated: Composition series require each subgroup to be normal in the next.

• Fundamental theorem of Galois theoryRelated: Normal subgroups correspond precisely to intermediate fields that are Galois over the base field.

• Normal extensionRelated: Under the Galois correspondence, normal intermediate extensions correspond to normal subgroups.

• Isomorphism theoremsRelated: Normality is what permits the quotient groups used throughout the theorems.

• Brauer–Suzuki theoremRelated: The structural argument forces central behavior incompatible with nonabelian simplicity.

• Fundamental theorem on homomorphismsRelated: A homomorphism's kernel is normal, so its cosets form a quotient group.