GroupTheory - Maple Programming Help

Online Help

All Products    Maple    MapleSim


Home : Support : Online Help : Mathematics : Group Theory : GroupTheory/DicyclicGroup

GroupTheory

  

DicyclicGroup

  

construct a dicyclic group as a permutation group or a finitely presented group

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

DicyclicGroup( n )

DicyclicGroup( n, s )

Parameters

n

-

algebraic; understood to be a positive integer

s

-

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

Description

• 

The dicyclic group is a non-abelian group of order 4n which contains a cyclic subgroup of order 2n for n>1.

• 

The DicyclicGroup( n ) command returns a dicyclic group, either as a permutation group (the default) or as a finitely presented group.

• 

You can specify the form of the group returned explicitly by passing one of the options 'form' = "permgroup" or 'form' = "fpgroup".

• 

If the parameter n is not a positive integer, then a symbolic group representing the dicyclic group of order 4*n 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:

DicyclicGroup6

1,2,3,45,6,7,89,10,11,1,7,3,52,6,4,89,11

(1)

DicyclicGroup6,form=permgroup

1,2,3,45,6,7,89,10,11,1,7,3,52,6,4,89,11

(2)

DicyclicGroup6,form=fpgroup

a,bb-1aba,a6b2,a12

(3)

IsNilpotentDicyclicGroup82kassumingk::'posint'

true

(4)

GDicyclicGroup6

G1,2,3,45,6,7,89,10,11,1,7,3,52,6,4,89,11

(5)

ZCenterG

ZZ1,2,3,45,6,7,89,10,11,1,7,3,52,6,4,89,11

(6)

GeneratorsZ

1,32,45,76,8

(7)

Compatibility

• 

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

• 

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

See Also

GroupTheory[CyclicGroup]

GroupTheory[MetacyclicGroup]