Linked from

The 40 pages that link to Group action, each with the reason it gives.

• Quotient groupNarrower topic: Orbits of group actions connect coset constructions to symmetry and counting.

• Orbit-stabilizer theoremNarrower topic: The theorem applies to each point in a set acted on by a group.

• Conjugacy classNarrower topic: Conjugation is an action of a group on itself.

• Invariant theoryNarrower topic: Invariants are defined by asking which quantities remain fixed under these transformations.

• Lagrange's theoremNarrower topic: Orbit-stabilizer generalizes the same divisibility argument from cosets to actions.

• Banach–Tarski paradoxNarrower topic: Rotations act on points of the sphere to organize the construction.

• Burnside's lemmaNarrower topic: The lemma applies to points moved by a group action.

• Cayley's theoremNarrower topic: Left multiplication is the action that produces the permutations in Cayley's construction.

• Fundamental theorem of Galois theoryNarrower topic: The Galois group acts on the extension, and fixed elements of its subgroups produce the paired fields.

• Icosahedral symmetryNarrower topic: It formalizes how icosahedral rotations act on vertices, faces, and other objects.

• Geometric group theoryNarrower topic: It is the basic way a group acts on a space.

• Vertex-transitive graphNarrower topic: Transitivity is the property that this action has a single orbit on vertices.

• Pólya enumeration theoremNarrower topic: The theorem counts configurations by identifying those related through this action.

• Poincaré groupNarrower topic: The group acts on spacetime events by combining linear maps and translations.

• Hausdorff paradoxNarrower topic: The proof organizes sphere rotations as a group acting on points and their orbits.

• Ping-pong lemmaNarrower topic: The lemma translates conditions on a group action into a conclusion about subgroup relations.

• Cheryl PraegerNarrower topic: Permutation groups arise precisely when a group acts on a set.