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GroupTheory

 AlternatingGroup

 Calling Sequence AlternatingGroup( n ) Alt( n )

Parameters

 n - a positive integer

Description

 • The alternating group ${\mathbf{A}}_{n}$ on $n$ elements is the set of all even permutations$\left\{1,2,\dots ,n\right\}$ for a positive integer $n$. The order of ${\mathbf{A}}_{n}$ is equal to n!/2, for n > 1. 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 ).

Examples

 > $\mathrm{with}\left(\mathrm{GroupTheory}\right):$
 > $G≔\mathrm{AlternatingGroup}\left(7\right)$
 ${G}{≔}{{\mathbf{A}}}_{{7}}$ (1)
 > $\mathrm{GroupOrder}\left(G\right)$
 ${2520}$ (2)
 > $\mathrm{IsTransitive}\left(G\right)$
 ${\mathrm{true}}$ (3)

Compatibility

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