Jordan's theorem (symmetric group)

In finite group theory, Jordan's theorem states that if a primitive permutation group G is a subgroup of the symmetric group S_n and contains a p-cycle for some prime number p < n − 2, then G is either the whole symmetric group S_n or the alternating group A_n. It was first proved by Camille Jordan.

The statement can be generalized to the case that p is a prime power.