GroupTheory/IsFinitelyGenerated - Maple Help
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GroupTheory

 IsFinitelyGenerated
 determine whether a group is finitely generated

 Calling Sequence IsFinitelyGenerated( G )

Parameters

 G - group

Description

 • A group $G$ is said to be finitely generated if it can be generated by a finite subset of its elements.
 • The IsFinitelyGenerated( G ) command returns true if the group G is finitely generated, and returns the value false otherwise.

Examples

 > $\mathrm{with}\left(\mathrm{GroupTheory}\right):$
 > $\mathrm{IsFinitelyGenerated}\left(\mathrm{PSp}\left(4,3\right)\right)$
 ${\mathrm{true}}$ (1)
 > $\mathrm{IsFinitelyGenerated}\left(\mathrm{Symm}\left(30\right)\right)$
 ${\mathrm{true}}$ (2)
 > $\mathrm{IsFinitelyGenerated}\left(\mathrm{QuasicyclicGroup}\left(37\right)\right)$
 ${\mathrm{false}}$ (3)
 > $\mathrm{IsFinitelyGenerated}\left(⟨⟨a,b⟩|\mathrm{.}\left({a}^{-2},{b}^{-2},{a}^{3},{b}^{3}\right)=1⟩\right)$
 ${\mathrm{true}}$ (4)