Linked from

The 21 pages that link to Permutation group, each with the reason it gives.

• Group theoryBroader topic: Permutations realize abstract groups as rearrangements of elements.

• Évariste GaloisNarrower topic: Galois used groups of root permutations to encode equations' symmetries.

• Cyclic groupCompared with: Many permutation groups are noncyclic, showing that groups need not have a single generator.

• Symmetric groupNarrower topic: Every symmetric group is the full permutation group on its underlying set.

• Niels Henrik AbelRelated: Permutations of polynomial roots provide the symmetry language behind the solvability question.

• Conjugacy classRelated: Permutations provide a concrete setting for computing conjugacy classes.

• Symmetry groupRelated: Symmetries of finite objects often act by permuting their vertices, edges, or components.

• Alternating groupNarrower topic: Aₙ is a permutation group consisting of exactly the even permutations.

• Camille JordanRelated: Jordan studied permutations as concrete representations of abstract groups.

• Burnside's lemmaRelated: Its permutations make the lemma's fixed points concrete.

• Ferdinand Georg FrobeniusRelated: Permutation actions provide concrete examples of the group representations central to Frobenius’s work.

• Inverse elementRelated: Each permutation has an inverse that restores the original arrangement.

• Slater determinantRelated: The determinant sums orbital assignments with signs given by particle permutations.

• Cayley's theoremRelated: Cayley's result links every abstract group to this concrete kind of group.

• Graph automorphismNarrower topic: Graph automorphisms are precisely the permutations that also preserve the graph’s structure.

• Pólya enumeration theoremNarrower topic: The symmetries being counted form a permutation group on the configuration’s positions.

• Rubik's CubeNarrower topic: Legal turns form permutations of the cube’s movable pieces.

• Particle statisticsRelated: Exchanges of identical particles form permutations whose representations classify allowed symmetries.

• Sliding puzzleRelated: Tile arrangements are permutations, though legal moves reach only a subset of them.

• SpeedcubingNarrower topic: Cube turns form a group, providing the algebraic structure behind legal configurations.

• Cheryl PraegerNarrower topic: This is the algebraic object at the heart of much of Praeger's research.