SymmetricGroup( n )
SymmetricGroup( n, form = f )
Symm( n )
Symm( n, form = f )
algebraic ; understood to be a positive integer
string ; either "permgroup" or "fpgroup"
The symmetric group Sn on n elements is the set of all permutations of1,2,…,n for a positive integer n.
The SymmetricGroup( n ) command returns a symmetric permutation group of degree n. The command Symm( n ) is also available as an abbreviation for SymmetricGroup( n ).
By default, a permutation group is returned. However, you can request that a finitely presented group isomorphic to the symmetric group of the indicated degree be returned by using the 'form' = "fpgroup" option. The default for the form option is 'form' = "permgroup".
If the degree n is not a positive integer, then a symbolic group representing the symmetric group of degree n is returned.
In the Standard Worksheet interface, you can insert this group into a document or worksheet by using the Group Constructors palette.
G ≔ Symm⁡4,'form'=fpgroup
G ≔ Symm⁡n
The GroupTheory[SymmetricGroup] command was introduced in Maple 17.
For more information on Maple 17 changes, see Updates in Maple 17.
The GroupTheory[SymmetricGroup] command was updated in Maple 2021.
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