TrivialGroup - Maple Help

GroupTheory

 TrivialGroup

 Calling Sequence TrivialGroup() TrivialGroup( form = F )

Description

 • 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.

Examples

 > $\mathrm{with}\left(\mathrm{GroupTheory}\right):$
 > $\mathrm{TrivialGroup}\left(\right)$
 $⟨⟩$ (1)
 > $\mathrm{GroupOrder}\left(\mathrm{TrivialGroup}\left(\right)\right)$
 ${1}$ (2)
 > $T≔\mathrm{TrivialGroup}\left('\mathrm{form}'="fpgroup"\right)$
 ${T}{≔}⟨{}{}{\mid }{}{}⟩$ (3)
 > $\mathrm{Generators}\left(T\right)$
 $\left[\right]$ (4)
 > $\mathrm{Relators}\left(T\right)$
 ${\varnothing }$ (5)

Compatibility

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