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.

References

• Griess, Robert L. (1998), Twelve sporadic groups, Springer, p. 5, ISBN 978-3-540-62778-4
• Isaacs, I. Martin (2008), Finite group theory, AMS, p. 245, ISBN 978-0-8218-4344-4
• Neuman, Peter M. (1975), "Primitive permutation groups containing a cycle of prime power length", Bulletin of the London Mathematical Society, 7 (3): 298–299, doi:10.1112/blms/7.3.298

External links

• Jordan's Symmetric Group Theorem on Mathworld