3.I.2B

Algebra and Geometry
Part IA, 2002

(a) What does it mean for a group to be cyclic? Give an example of a finite abelian group that is not cyclic, and justify your assertion.

(b) Suppose that GG is a finite group of rotations of R2\mathbb{R}^{2} about the origin. Is GG necessarily cyclic? Justify your answer.