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GroupTheory

 IsCyclic
 attempt to determine whether a group is cyclic

 Calling Sequence IsCyclic( G )

Parameters

 G - a group

Description

 • A group $G$ is cyclic if it can be generated by a single element.
 • The IsCyclic( G ) command attempts to determine whether the group G is cyclic.  It returns true if G is cyclic and returns false otherwise. The command may return FAIL on (most) finitely presented groups.

Examples

 > $\mathrm{with}\left(\mathrm{GroupTheory}\right):$
 > $G≔\mathrm{SmallGroup}\left(6,1\right):$
 > $\mathrm{IsCyclic}\left(G\right)$
 ${\mathrm{false}}$ (1)
 > $\mathrm{IsCyclic}\left(\mathrm{SmallGroup}\left(6,2\right)\right)$
 ${\mathrm{true}}$ (2)
 > $G≔⟨a|{a}^{6}=1⟩$
 ${G}{≔}⟨{}{a}{}{\mid }{}{{a}}^{{6}}{}⟩$ (3)
 > $\mathrm{IsCyclic}\left(G\right)$
 ${\mathrm{true}}$ (4)

Compatibility

 • The GroupTheory[IsCyclic] command was introduced in Maple 2015.