jordan, theorem, symmetric, group, finite, group, theory, jordan, theorem, states, that, primitive, permutation, group, subgroup, symmetric, group, contains, cycle, some, prime, number, then, either, whole, symmetric, group, alternating, group, first, proved, . In finite group theory Jordan s theorem 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 lt n 2 then G is either the whole symmetric group Sn or the alternating group An It was first proved by Camille Jordan The statement can be generalized to the case that p is a prime power References editGriess 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 Neumann 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 archived from the original on 2013 04 15External links editJordan s Symmetric Group Theorem on Mathworld nbsp This group theory related article is a stub You can help Wikipedia by expanding it vte Retrieved from https en wikipedia org w index php title Jordan 27s theorem symmetric group amp oldid 1170058321, wikipedia, wiki, book, books, library,
