IsTrivial - Maple Help
For the best experience, we recommend viewing online help using Google Chrome or Microsoft Edge.

GroupTheory

 IsTrivial
 attempt to determine whether a group is trivial

 Calling Sequence IsTrivial( G )

Parameters

 G - a group

Description

 • A group $G$ is said to be trivial if it consists of only an identity element, that is, it has order equal to $1$.
 • The IsTrivial( G ) command attempts to determine whether the group G is trivial.  It returns true if G is trivial and returns false otherwise. The command may raise an exception on (most) finitely presented groups.

Examples

 > $\mathrm{with}\left(\mathrm{GroupTheory}\right):$
 > $G≔\mathrm{SmallGroup}\left(1,1\right)$
 ${G}{≔}⟨⟩$ (1)
 > $\mathrm{IsTrivial}\left(G\right)$
 ${\mathrm{true}}$ (2)
 > $\mathrm{IsTrivial}\left(\mathrm{SmallGroup}\left(32,5\right)\right)$
 ${\mathrm{false}}$ (3)
 > $G≔⟨a|{a}^{6}=1⟩$
 ${G}{≔}⟨{}{a}{}{\mid }{}{{a}}^{{6}}{}⟩$ (4)
 > $\mathrm{IsTrivial}\left(G\right)$
 ${\mathrm{false}}$ (5)
 > $\mathrm{IsTrivial}\left(⟨⟨a,b⟩|⟨{a}^{2},{b}^{3},{\left(\mathrm{.}\left(a,b\right)\right)}^{5}=1⟩⟩\right)$
 ${\mathrm{false}}$ (6)
 > $\mathrm{IsTrivial}\left(⟨⟨a,b⟩|⟨{a}^{2}={b}^{3},{b}^{2}=a⟩⟩\right)$
 ${\mathrm{true}}$ (7)

Compatibility

 • The GroupTheory[IsTrivial] command was introduced in Maple 2019.
 • For more information on Maple 2019 changes, see Updates in Maple 2019.