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GroupTheory

  

DihedralGroup

  

construct a dihedral group of a given degree

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

DihedralGroup( n )

DihedralGroup( n, s )

Parameters

n

-

a positive integer

s

-

(optional) equation of the form form = "fpgroup" or form = "permgroup" (default)

Description

• 

The dihedral group of degree n is the symmetry group of an n-sided regular polygon for n>2. It is generated by a reflection (of order 2), and a rotation (of order n). It acts as a permutation group on the vertices of the regular n-sided polygon.

• 

For n=1, the dihedral group is a cyclic group of order 2.  For n=2, the dihedral group is the non-cyclic group of order 4, also known as the Klein 4-group.

• 

The DihedralGroup( n ) command returns a dihedral group, either as a permutation group or a group defined by generators and defining relations. By default, a permutation group is returned, but a finitely presented group can be requested by passing the option 'form' = "fpgroup".

• 

If the value of the parameter n is not numeric, then a symbolic group representing the dihedral group of the indicated degree is returned.

• 

In the Standard Worksheet interface, you can insert this group into a document or worksheet by using the Group Constructors palette.

Examples

withGroupTheory:

DihedralGroup13

D13

(1)

DihedralGroup13,form=fpgroup

D13

(2)

DihedralGroup13,form=permgroup

D13

(3)

GroupOrderDihedralGroup3k

6k

(4)

IsNilpotentDihedralGroup6kassumingk::'posint'

false

(5)

Compatibility

• 

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

• 

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

See Also

GroupTheory[DicyclicGroup]

GroupTheory[GroupOrder]

GroupTheory[IsNilpotent]