AlternatingGroup - Maple Help
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GroupTheory

  

AlternatingGroup

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

AlternatingGroup( n, formopt )

Alt( n, formopt )

Parameters

n

-

algebraic; understood to be a positive integer

formopt

-

(optional) equation of the form form = F, where F is either "permgroup" (the default) or "fpgroup"

Description

• 

The alternating group  on  elements is the set of all even permutations of for a positive integer . The order of  is equal to , for . The alternating group of degree  is simple if  is at least .

• 

The AlternatingGroup( n ) command returns an alternating permutation group of degree n.  You can also use Alt( n ) as an abbreviation of AlternatingGroup( n ).

• 

The form = F option controls the form of the group returned. By default, a permutation group is returned; this is equivalent to passing the option form = "permgroup". A finitely presented group can be obtained by passing the option form = "fpgroup".

• 

If the argument n is not an integer constant, then a symbolic group is returned. In this case, the form option is ignored.

• 

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)

If the argument to the constructor is not a literal integer, then a symbolic group is returned.

(9)

(10)

(11)

Compatibility

• 

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

• 

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

See Also

GroupTheory[DrawSubgroupLattice]

GroupTheory[GroupOrder]

GroupTheory[IsPrimitive]

GroupTheory[IsSimple]

GroupTheory[IsTransitive]

GroupTheory[SymmetricGroup]

 


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