The trivial group is the unique (up to isomorphism) group of order $1$.

The TrivialGroup() command returns a trivial group.

The form = F option controls the type of group returned. By default, a permutation group (with empty generating set) is returned; this is the same as using the form = "permgroup" option. If the form = "fpgroup" option is passed, then a trivial finitely presented group is returned, with empty sets of generators and relators. Finally, you can explicitly request a symbolic trivial group by using the form = "symbolic" option.

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

$\mathrm{TrivialGroup}\left(\right)$

$\mathrm{GroupOrder}\left(\mathrm{TrivialGroup}\left(\right)\right)$

$1$

$T≔\mathrm{TrivialGroup}\left('\mathrm{form}'=''fpgroup''\right)$

$T≔⟨\mid ⟩$

$\mathrm{Generators}\left(T\right)$

$\mathrm{Relators}\left(T\right)$

$\varnothing$

The GroupTheory[TrivialGroup] command was introduced in Maple 17.

For more information on Maple 17 changes, see Updates in Maple 17.