I read from some physics books that the 2D rotation can be expressed in exponential form:
$$R(\theta) = e^{X(\theta)}, \theta \in R $$
In physics, X relates to the momentum of a particle, and is defined to be the generator of the rotation. Some authors also state that X is the generator of the rotation group .
Is that statement correct, and if it is, can we consider the rotation group ($N\ge2$) as a cyclic group. As if I understand correctly, only cyclic groups have a generator.