IsTransitive - Maple Help
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GroupTheory

  

IsTransitive

  

determine whether a permutation group is transitive

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

IsTransitive( G, domain )

Parameters

G

-

a permutation group

domain

-

(optional) a stable set (or list) of positive integers

Description

• 

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.

Examples

withGroupTheory:

The following group is not transitive because it has two orbits.

GPermutationGroupPerm1,2,Perm1,2,3,4,5

G1,2,1,2,34,5

(1)

IsTransitiveG

false

(2)

OrbitsG

11,2,1,2,34,5,41,2,1,2,34,5

(3)

However, it is transitive on each of its orbits.

IsTransitiveG,1,2,3

true

(4)

IsTransitiveG,4,5

true

(5)

GPermutationGroupPerm1,5,Perm1,3,5

G1,3,5,1,5

(6)

IsTransitiveG

true

(7)

IsTransitiveG,1,2,3,4,5

false

(8)

IsTransitiveAlt10

true

(9)

IsTransitiveFrobeniusGroup12822,2

true

(10)

Compatibility

• 

The GroupTheory[IsTransitive] command was introduced in Maple 17.

• 

For more information on Maple 17 changes, see Updates in Maple 17.

See Also

GroupTheory

GroupTheory[AlternatingGroup]

GroupTheory[FrobeniusGroup]

GroupTheory[Orbit]

GroupTheory[PermutationGroup]

GroupTheory[Transitivity]

 


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