In my text it says $\{e^{i\theta}:\theta\in\mathbb{R}\}$ is a subgroup but it did not clarify the subgroup of which group.
Furthermore I remember this entire set as being a semigroup, is there a difference between a subgroup and semigroup?
[Math] the difference between a subgroup and semigroup
group-theoryterminology
Best Answer
A subgroup is a subset of a group that is itself closed under the group operation.
A semigroup is a set equipped with an operation that is merely associative, different from a group in that we assume the binary operation of a group is associative and invertible, i.e. each element has an inverse with respect to the operation.