IsElementary - Maple Help

GroupTheory

 IsElementary
 attempt to determine whether a group is elementary Abelian

 Calling Sequence IsElementary( G )

Parameters

 G - a permutation group

Description

 • A group $G$ is elementary if it is a finite Abelian group with prime exponent. Equivalently, $G$ is elementary if it is a direct sum (product) of groups each of order equal to a fixed prime $p$.
 • The IsElementary( G ) command attempts to determine whether the group G is elementary.  It returns true if G is elementary and returns false otherwise.
 • The group G must be an instance of a permutation group.

Examples

 > $\mathrm{with}\left(\mathrm{GroupTheory}\right):$
 > $G≔\mathrm{SmallGroup}\left(32,1\right):$
 > $\mathrm{IsElementary}\left(G\right)$
 ${\mathrm{false}}$ (1)
 > $G≔\mathrm{SmallGroup}\left(17,1\right):$
 > $\mathrm{IsElementary}\left(G\right)$
 ${\mathrm{true}}$ (2)

Compatibility

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