In finite group theory, Jordan's theorem states that if a primitive permutation group G is a subgroup of the symmetric group S<sub>n</sub> and contains a p-cycle for some prime number p < n − 2, then G is either the whole symmetric group S<sub>n</sub> or the alternating group A<sub>n</sub>. It was first proved by Camille Jordan.
The statement can be generalized to the case that p is a prime power.