Jordan's theorem is a statement in finite group theory. It states that if a primitive permutation group G is a subgroup of the symmetric group Sn and contains a p-cycle for some prime number p < n − 2, then G is either the whole symmetric group Sn or the alternating group An.
The statement can be generalized to the case that p is a prime power.
References
Jordan's theorem (symmetric group) Wikipedia(Text) CC BY-SA