Linked from

The 25 pages that link to Galois group, each with the reason it gives.

• GroupBroader topic: Its structure encodes which polynomial roots can be expressed using radicals.

• Field extensionRelated: Its structure records how the extension’s elements can be permuted while preserving the base.

• Finite groupRelated: Finite Galois groups encode symmetries of algebraic equations and their roots.

• SubgroupRelated: Its subgroups correspond to intermediate fields in the fundamental theorem of Galois theory.

• Évariste GaloisBroader topic: Its structure reveals whether an equation's roots can be expressed by radicals.

• Permutation groupRelated: Its action on polynomial roots realizes a central permutation-group example.

• Symmetric groupRelated: Galois groups act by permuting polynomial roots, sometimes as subgroups of Sₙ.

• Cyclotomic fieldRelated: Automorphisms describe the symmetries of a cyclotomic field.

• Galois theoryRelated: Its structure records the symmetries among roots that Galois theory studies.

• Discriminant (polynomial)Related: The discriminant’s square class constrains whether the Galois group consists of even permutations.

• Splitting fieldBroader topic: For a separable polynomial, its splitting field’s automorphisms encode root permutations.

• Class field theoryNarrower topic: Class field theory characterizes abelian extensions through their Galois groups.

• Abel–Ruffini theoremRelated: The general quintic’s Galois group fails the condition required for radical solutions.

• Field automorphismBroader topic: It collects precisely the extension symmetries used to study solvability and intermediate fields.

• Fundamental theorem of Galois theoryRelated: Subgroups of this group form one side of the theorem’s correspondence.

• Inverse Galois problemNarrower topic: The problem asks which finite groups can arise as these symmetry groups.

• Solvability by radicalsRelated: Its group structure determines whether the polynomial’s roots admit radical expressions.

• Normal extensionRelated: For finite normal separable extensions, its automorphisms capture all base-field embeddings.

• Chebotarev density theoremNarrower topic: The density is computed from the size of a conjugacy class within this group.

• Gauss–Wantzel theoremRelated: The symmetry structure of roots of unity explains why powers of two govern constructibility.

• Kronecker–Weber theoremNarrower topic: The theorem concerns extensions whose Galois groups are abelian.

• Primitive element theoremRelated: A primitive element lets the extension’s conjugates be studied through its Galois group.

• DiscriminantRelated: Polynomial discriminant sign and square class constrain the Galois group’s action on roots.

• Robert LanglandsRelated: Galois groups encode the symmetries of number fields central to the program.

• Schinzel's theoremRelated: Its action on polynomial roots helps characterize primes where a root appears after reduction.