ElementaryGroup( p, n )
ElementaryGroup( p, n, form = f )
algebraic; understood to represent a prime number
algebraic; understood to represent a positive integer
string ; either "permgroup" or "fpgroup"
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.
If either of p and n is not an explicit integer, then a symbolic group representing the elementary group of order pn is returned.
In the Standard Worksheet interface, you can insert this group into a document or worksheet by using the Group Constructors palette.
G ≔ ElementaryGroup⁡3,4
G ≔ ElementaryGroup⁡3,5,'form'=fpgroup
G ≔ ElementaryGroup⁡17,3
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.
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