Linked from

The 20 pages that link to Symmetric group, each with the reason it gives.

• PermutationBroader topic: It organizes every permutation of an n-element set as one algebraic structure.

• Configuration spaceRelated: Its action on product coordinates turns labeled configurations into unlabeled ones.

• Finite groupBroader topic: It provides a concrete model of finite groups through permutations.

• Quotient groupRelated: Quotients of permutation groups encode symmetries after a normal subgroup is collapsed.

• Permutation groupBroader topic: It is the largest permutation group on a given finite set.

• Galois theoryCompared with: Generic polynomials often have full symmetric groups, which obstruct radical solutions in high degree.

• Abelian groupCompared with: Most symmetric groups are non-Abelian, contrasting with commutative group structure.

• Orbit-stabilizer theoremRelated: Its natural action on points illustrates how orbit size depends on the stabilizer.

• Conjugacy classBroader topic: In this group, conjugacy classes are classified by cycle type.

• Alternating groupRelated: Aₙ is the index-two subgroup of Sₙ formed by even permutations.

• Composition seriesBroader topic: Its composition factors illustrate how a nonabelian simple group can occur.

• Cayley's theoremNarrower topic: The theorem embeds a group into the symmetric group on its own elements.

• Permutation matrixRelated: Permutation matrices of a fixed size represent the elements of this group.

• Solvable groupBroader topic: The symmetric group on five or more symbols is a standard nonsolvable example.

• Abel–Ruffini theoremRelated: The generic degree-five polynomial has the nonsolvable symmetric group S₅ as its Galois group.

• Finite cyclic groupCompared with: Symmetric groups of degree at least three are generally noncyclic, unlike every finite cyclic group.

• Inverse Galois problemBroader topic: Symmetric groups arise as Galois groups of generic polynomials and many specific polynomials.

• Newton's identitiesNarrower topic: Permutation symmetry is the underlying reason the variables enter through symmetric polynomials.

• Young tableauRelated: Its irreducible representations are indexed by partitions and modeled using tableaux.

• Algebraic combinatoricsRelated: Its representations organize the symmetries and statistics of many combinatorial objects.