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GroupTheory

  

IsDihedral

  

determine whether a permutation group is a dihedral group

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

IsDihedral( G )

Parameters

 G

-

a permutation group

Description

• 

The IsDihedral( G ) command determines whether the finite group G is isomorphic to a dihedral group of some (even) order, without using an (expensive) isomorphism test. It returns the value true if G is isomorphic to Dn, for some positive integer n, and returns false otherwise.

Examples

withGroupTheory:

GGroupPerm1,2,3,4,5,6,7,8,9,10,11,12,13,14,Perm2,7,3,6,4,5,9,14,10,13,11,12

G1,2,3,4,5,6,78,9,10,11,12,13,14,2,73,64,59,1410,1311,12

(1)

GroupOrderG

14

(2)

IsDihedralG

true

(3)

AreIsomorphicG,DihedralGroup7

true

(4)

IsDihedralQuaternionGroup

false

(5)

Compatibility

• 

The GroupTheory[IsDihedral] command was introduced in Maple 2019.

• 

For more information on Maple 2019 changes, see Updates in Maple 2019.

See Also

GroupTheory

GroupTheory[AreIsomorphic]

GroupTheory[DihedralGroup]

GroupTheory[Group]

GroupTheory[GroupOrder]

GroupTheory[QuaternionGroup]