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GroupTheory

  

CyclicGroup

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

CyclicGroup( n )

CyclicGroup( n, s )

Parameters

n

-

a positive integer or infinity

s

-

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

Description

• 

A cyclic group is an abelian group generated by a single element. The CyclicGroup command returns a group, either as a permutation group, or a group defined by a generator and a relator, isomorphic to a cyclic group of order n.

• 

By default, a permutation group is returned if n is finite, but you can specify that the cyclic group of order n be constructed as a finitely presented group by passing the option form = "fpgroup".

• 

If n = infinity, then a finitely presented group is returned. It is an error to specify form = permgroup if the argument n is equal to infinity.

• 

You can use the mindegree option to create cyclic permutation groups of much larger order than would be possible without this option. By default, mindegree = false but, if you pass mindegree = true (or just mindegree), then a permutation group of minimal degree which is cyclic of the indicated order is returned.

Examples

withGroupTheory:

CyclicGroup14

C14

(1)

CyclicGroup14,'form'=permgroup

C14

(2)

CyclicGroup14,'form'=fpgroup

gg14

(3)

CyclicGroup∞

g0

(4)

DegreeCyclicGroup12

12

(5)

DegreeCyclicGroup12,':-mindegree'

7

(6)

CyclicGroup273757

Error, (in GroupTheory:-CyclicGroup) object too large

GCyclicGroup273757,':-mindegree'

G:=C21870000000

(7)

DegreeG

80440

(8)

Compatibility

• 

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

• 

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

See Also

GroupTheory[DicyclicGroup]

GroupTheory[MetacyclicGroup]

 


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