GroupTheory[ElementaryGroup] - Maple Help

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GroupTheory[ElementaryGroup]

Calling Sequence

ElementaryGroup( p, n )

ElementaryGroup( p, n, form = f )

Parameters

p

-

a prime number

n

-

a positive integer

f

-

: string : either "permgroup" or "fpgroup"

Description

• 

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

• 

The ElementaryGroup( p, n ) command returns an elementary Abelian group of order pn, 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.

Examples

withGroupTheory:

G:=ElementaryGroup3,4

G:=C34

(1)

GroupOrderG

81

(2)

IsAbelianG

true

(3)

GeneratorsG

1,2,3,4,5,6,7,8,9,10,11,12

(4)

G:=ElementaryGroup3,5,'form'=fpgroup

G:=C35

(5)

G:=ElementaryGroup17,3

G:=C173

(6)

GroupOrderG

4913

(7)

See Also

GroupTheory, GroupTheory[CyclicGroup], GroupTheory[Generators], GroupTheory[GroupOrder], GroupTheory[IsAbelian]


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