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GroupTheory

  

SymmetricGroup

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

SymmetricGroup( n )

SymmetricGroup( n, form = f )

Symm( n )

Symm( n, form = f )

Parameters

n

-

algebraic ; understood to be a positive integer

f

-

string ; either "permgroup" or "fpgroup"

Description

• 

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.

Examples

withGroupTheory:

SymmetricGroup7

S7

(1)

GroupOrderSymmetricGroup5

120

(2)

IsPrimitiveSymm11

true

(3)

GSymm4,form=fpgroup

GS4

(4)

GSymmn

GSn

(5)

GroupOrderG

n!

(6)

IsSolubleGassumingn<5

true

(7)

Compatibility

• 

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

• 

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

See Also

GroupTheory[AlternatingGroup]

GroupTheory[GroupOrder]

GroupTheory[IsPrimitive]