 GroupTheory - Maple Programming Help

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GroupTheory

 IsFinite
 determine whether a group is finite

 Calling Sequence IsFinite( G )

Parameters

 G - a group data structure

Description

 • The IsFinite command attempts to determine whether the group G is finite.
 • For permutation groups and Cayley table groups this is simply a property of the class of the group, but for matrix groups and finitely presented groups the question is algorithmically undecidable, in general. Nevertheless, the IsFinite command attempts to determine whether the group is finite or infinite, and returns true or false, respectively, if it can determine the answer.  If IsFinite cannot determine whether the input group G is finite, it returns the value FAIL.

Examples

 > $\mathrm{with}\left(\mathrm{GroupTheory}\right):$
 > $\mathrm{IsFinite}\left(\mathrm{Alt}\left(4\right)\right)$
 ${\mathrm{true}}$ (1)
 > $\mathrm{IsFinite}\left(\mathrm{CyclicGroup}\left(\mathrm{\infty }\right)\right)$
 ${\mathrm{false}}$ (2)

Compatibility

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