The trivial group, a group consisting of a single element, which should not be confused with the empty set (which has no elements, and lacking an identity element, cannot be a group), is the same as the similarly defined trivial monoid.
In mathematics, a trivial group or zero group is a group consisting of a single element. The similarly defined trivial monoid is also a group since its only element is its own inverse, and is hence the same as the trivial group. The trivial group should not be confused with the empty set (which has no elements, and lacking an identity element, cannot be a group). 
