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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

-

a positive integer

s

-

optional equation: form = "fpgroup" or form = "permgroup" (default)

Description

• 

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

• 

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.

Examples

withGroupTheory&colon;

DicyclicGroup6

1&comma;2&comma;3&comma;45&comma;6&comma;7&comma;89&comma;10&comma;11&comma;1&comma;7&comma;3&comma;52&comma;6&comma;4&comma;89&comma;11

(1)

DicyclicGroup6&comma;&apos;form&apos;&equals;permgroup

1&comma;2&comma;3&comma;45&comma;6&comma;7&comma;89&comma;10&comma;11&comma;1&comma;7&comma;3&comma;52&comma;6&comma;4&comma;89&comma;11

(2)

DicyclicGroup6&comma;&apos;form&apos;&equals;fpgroup

a&comma;bb-1aba&comma;a6b2&comma;a12

(3)

IsNilpotentDicyclicGroup82kassumingk::posint

true

(4)

GDicyclicGroup6

G:=1&comma;2&comma;3&comma;45&comma;6&comma;7&comma;89&comma;10&comma;11&comma;1&comma;7&comma;3&comma;52&comma;6&comma;4&comma;89&comma;11

(5)

ZCenterG

Z:=Z1&comma;2&comma;3&comma;45&comma;6&comma;7&comma;89&comma;10&comma;11&comma;1&comma;7&comma;3&comma;52&comma;6&comma;4&comma;89&comma;11

(6)

GeneratorsZ

1&comma;32&comma;45&comma;76&comma;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]

 


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