AlternatingGroup( n, formopt )
Alt( n, formopt )
algebraic; understood to be a positive integer
(optional) equation of the form form = F, where F is either "permgroup" (the default) or "fpgroup"
The alternating group An on n elements is the set of all even permutations of1,2,…,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.
G ≔ AlternatingGroup⁡7
G ≔ Alt⁡4
G ≔ Alt⁡5,'form'=fpgroup
If the argument to the constructor is not a literal integer, then a symbolic group is returned.
G ≔ Alt⁡3⁢n+7
The GroupTheory[AlternatingGroup] command was introduced in Maple 17.
For more information on Maple 17 changes, see Updates in Maple 17.
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