Linked from

The 16 pages that link to Orbit-stabilizer theorem, each with the reason it gives.

• Group actionRelated: It connects the two basic measurements produced by an action.

• Group theoryRelated: It connects how a group moves objects to the subgroup that fixes them.

• Finite groupRelated: It converts symmetry into a counting equation for finite groups.

• Permutation groupRelated: It connects the sizes of a permutation group’s orbits and point stabilizers.

• CosetRelated: The orbit can be identified with cosets of the point stabilizer.

• Conjugacy classRelated: It gives the class-size formula from the centralizer's index.

• Lagrange's theoremRelated: Applying it to the action of a group on itself recovers Lagrange’s theorem.

• Rotational symmetryRelated: It connects the number of rotated positions to the rotations that preserve an object.

• Sylow theoremsRelated: Applied to conjugation, it converts the number of conjugates into an index.

• Burnside's lemmaRelated: It supplies a complementary way to relate orbit sizes and stabilizers.

• Graph automorphismRelated: It connects how automorphisms move a vertex to the subgroup that fixes it.

• Vertex-transitive graphRelated: It connects the number of vertices to the automorphisms fixing one vertex.

• CentralizerRelated: Conjugation turns the centralizer into the stabilizer in this counting formula.

• Pólya enumeration theoremRelated: It explains orbit sizes but does not by itself give Pólya’s color-inventory counts.

• Muirhead's inequalityRelated: Permutation counts clarify the normalization of sums over distinct exponent permutations.

• Fundamental theorem on homomorphismsRelated: The orbit map is a homomorphism from a group quotient onto an orbit when the action is transitive.