gives the order of permutation perm.
Examplesopen allclose all
Group elements with order 2 are called involutions. If all elements of a group (except the identity) have order 2, then the group is Abelian (the opposite implication does not hold). This group is Abelian:
Properties & Relations (6)
By Lagrange's theorem, the order of each element of a finite group divides the order of the group. However, not all divisors of the order of a group correspond to the order of some element in the group. Take the alternating group of degree 4, which has order 12, and hence divisors 6, 3, 2:
Wolfram Research (2010), PermutationOrder, Wolfram Language function, https://reference.wolfram.com/language/ref/PermutationOrder.html.
Wolfram Language. 2010. "PermutationOrder." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/PermutationOrder.html.
Wolfram Language. (2010). PermutationOrder. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/PermutationOrder.html