GroupTheory
IsTransitive
determine whether a permutation group is transitive
Calling Sequence
Parameters
Description
Examples
Compatibility
IsTransitive( G )
G
-
a permutation group
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 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.
with⁡GroupTheory:
G≔PermutationGroup⁡1,2,1,2,3,4,5
G≔1,2,1,2,34,5
IsTransitive⁡G
false
IsTransitive⁡AlternatingGroup⁡4
true
The GroupTheory[IsTransitive] command was introduced in Maple 17.
For more information on Maple 17 changes, see Updates in Maple 17.
See Also
GroupTheory[Orbit]
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