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GroupTheory

  

Transitivity

  

compute the transitivity of a permutation group

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

Transitivity( G )

Parameters

G

-

a permutation group

Description

• 

The transitivity of a permutation group G is the largest non-negative integer k for which G is k-transitive. In other words, the transitivity of G is k if G is k-transitive, but not k+1-transitive. (By convention, the transitivity of an intransitive group is equal to 0.)

• 

The Transitivity( G ) command returns the transitivity of the permutation group G. The group G must be an instance of a permutation group.

Examples

withGroupTheory:

TransitivityAlt4

2

(1)

TransitivitySymm4

4

(2)

TransitivityAlt5

3

(3)

TransitivitySymm5

5

(4)

TransitivityMathieuGroup23

4

(5)

Compatibility

• 

The GroupTheory[Transitivity] command was introduced in Maple 2016.

• 

For more information on Maple 2016 changes, see Updates in Maple 2016.

See Also

GroupTheory

GroupTheory[AlternatingGroup]

GroupTheory[IsTransitive]

GroupTheory[MathieuGroup]

GroupTheory[Orbit]

GroupTheory[SymmetricGroup]