Yes. I quote from Group (mathematics) - Wikipedia, the free encyclopedia:

"A trivial group is a group consisting of a single element. All such groups are isomorphic so one often speaks of the trivial group. The single element of the trivial group, variously labeled e, 1, or 0, is the identity element. The group operation is e + e = e."

See also Trivial Group -- from Wolfram MathWorld