ElementaryGroup - Maple Help
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GroupTheory

  

ElementaryGroup

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

ElementaryGroup( p, n )

ElementaryGroup( p, n, form = f )

Parameters

p

-

algebraic; understood to represent a prime number

n

-

algebraic; understood to represent a positive integer

f

-

string ; either "permgroup" or "fpgroup"

Description

• 

An elementary Abelian group of order , where  is a prime number, is a direct product (or direct sum) of  copies of the cyclic group of order .

• 

The ElementaryGroup( p, n ) command returns an elementary Abelian group of order , either as a permutation group or as a finitely presented group, according to the value of the form option. By default, a permutation group is returned.

• 

If either of p and n is not an explicit integer, then a symbolic group representing the elementary group of order  is returned.

• 

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

Examples

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

Compatibility

• 

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

• 

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

• 

The GroupTheory[ElementaryGroup] command was updated in Maple 2020.

See Also

GroupTheory

GroupTheory[CyclicGroup]

GroupTheory[Generators]

GroupTheory[GroupOrder]

GroupTheory[IsAbelian]

 


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