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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 An on n elements is the set of all even permutations of1&comma;2&comma;&comma;n for a positive integer n. The order of An is equal to n!2, for 1<n. The alternating group of degree n is simple if n is at least 5.

• 

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

withGroupTheory&colon;

GAlternatingGroup7

GA7

(1)

GroupOrderG

2520

(2)

IsTransitiveG

true

(3)

IsPrimitiveG

true

(4)

IsSimpleG

true

(5)

GAlt4

GA4

(6)

IsSimpleG

false

(7)

DrawSubgroupLatticeG

GAlt5&comma;form=fpgroup

Gs&comma;ts3&comma;t3&comma;ts-1tsts-1ts&comma;ststststst

(8)

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

GAlt3n+7

GA3n+7

(9)

IsSimpleGassumingn::&apos;posint&apos;

true

(10)

GroupOrderG

3n+7!2

(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]