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.

$\mathrm{with}\left(\mathrm{GroupTheory}\right)\:$

$G≔\mathrm{SmallGroup}\left(1\,1\right)$

$G≔⟨⟩$

$\mathrm{IsTrivial}\left(G\right)$

$\mathrm{true}$

$\mathrm{IsTrivial}\left(\mathrm{SmallGroup}\left(32\,5\right)\right)$

$\mathrm{false}$

$G≔⟨a|a^6=1⟩$

$G≔⟨a\mid a^6⟩$

$\mathrm{IsTrivial}\left(G\right)$

$\mathrm{false}$

$\mathrm{IsTrivial}\left(⟨⟨a\,b⟩|⟨a^2\,b^3\,{\left(a·b\right)}^5=1⟩⟩\right)$

$\mathrm{false}$

$\mathrm{IsTrivial}\left(⟨⟨a\,b⟩|⟨a^2=b^3\,b^2=a⟩⟩\right)$

$\mathrm{true}$

The GroupTheory[IsTrivial] command was introduced in Maple 2019.

For more information on Maple 2019 changes, see Updates in Maple 2019.