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GroupTheory

  

IsRegular

  

determine whether a permutation group is regular

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

IsRegular( G )

Parameters

G

-

a permutation group

Description

• 

A permutation group G (acting on the set1,2,,n is regular if it is transitive and the stabilizer of any point is trivial. This means that the action of G is permutation isomorphic  to the action of G on itself by (right) translation.

• 

Every Abelian transitive group is regular.

• 

The IsRegular( G ) command returns true if the permutation group G is regular, and returns false otherwise. The group G must be an instance of a permutation group.

Examples

withGroupTheory:

GGroupPerm1,2,Perm1,2,3,4,5

G1,2,1,2,34,5

(1)

IsRegularG

false

(2)

IsRegularCyclicGroup6

true

(3)

IsRegularCyclicGroup6,:-mindegree

false

(4)

Compatibility

• 

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

• 

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

See Also

GroupTheory

GroupTheory[IsTransitive]

GroupTheory[Stabilizer]