Linked from

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

• Group theoryRelated: Group actions make abstract group operations act on concrete objects.

• Lie groupRelated: Lie groups commonly express their symmetries through smooth actions.

• GroupRelated: Group actions turn abstract group elements into symmetries of concrete objects.

• Galois groupRelated: Galois group elements act on extension elements and, especially, polynomial roots.

• Group homomorphismRelated: A group action is equivalent to a homomorphism into a permutation group.

• Finite groupRelated: Actions turn abstract finite groups into concrete permutations.

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

• Invariant (mathematics)Related: Group actions specify the transformations against which many invariants are defined.

• Permutation groupRelated: A permutation group acts naturally on the set its permutations rearrange.

• Point groupRelated: It formalizes how point-group operations transform points in space.

• Group representationCompared with: A group action needs only a set, whereas a representation requires linear transformations.

• CosetRelated: Multiplication translates a subgroup as a set within the group.

• 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.

• Symmetry groupRelated: Symmetries act on the object's points, states, or other structural elements.

• Alternating groupRelated: Aₙ acts naturally on the underlying n-element set.

• Scalar multiplicationRelated: Nonzero scalars act on vectors by scaling, illustrating a group action.

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

• Camille JordanRelated: Group actions connect permutation methods to the broader abstract language Jordan helped develop.

• Sylow theoremsRelated: Orbit counting supplies a standard proof of Sylow existence and the counting congruence.

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

• Crystallographic point groupRelated: A point group acts on directions and positions around its fixed point.

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

• Algebraic structureRelated: It relates a group structure to a different set rather than adding operations on one set.

• 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.

• Erlangen programRelated: A group acts on the points or structures whose geometry is being classified.

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

• Rotation groupRelated: It describes how a rotation group acts on the points of an object.

• 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.

• Wigner's theoremRelated: Physical symmetries usually form groups acting on quantum state rays.

• 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.

• Brauer–Suzuki theoremRelated: Permutation actions provide tools for translating subgroup structure into global constraints.

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

• Fundamental theorem on homomorphismsRelated: Orbit maps often yield quotient descriptions through their kernels.