determine whether a permutation group is transitive
IsTransitive( G, domain )
a permutation group
(optional) a stable set (or list) of positive integers
A permutation group G (acting on the set1,2,…,n is transitive if, for any α and β, there is a permutation g in G for which αg=β. Alternatively, G is transitive if it has precisely one orbit.
The domain argument, which is optional and is, by default, equal to the support of G, specifies a stable set under the action of G on which to test the transitivity of G.
The IsTransitive( G ) command returns true if the permutation group G is transitive, and returns false otherwise. The group G must be an instance of a permutation group.
The following group is not transitive because it has two orbits.
G ≔ PermutationGroup⁡Perm⁡1,2,Perm⁡1,2,3,4,5
However, it is transitive on each of its orbits.
G ≔ PermutationGroup⁡Perm⁡1,3,5,Perm⁡1,5
The GroupTheory[IsTransitive] command was introduced in Maple 17.
For more information on Maple 17 changes, see Updates in Maple 17.
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