Categories

# List all proper, non-trivial subgroups of $U_6$ where $U_6$ is the group of $6$th roots of unity. Also, list the generators.

A) List all proper, non-trivial subgroups of $$U_6$$ where $$U_6$$ is the group of $$6$$th roots of unity:

So 6th roots of unity are $$\pm1, \pm \frac{1}{2} \pm \frac{\sqrt{3}}2i$$ How do these relate to the subgroups?

B) List the generators:

If I am not mistaken the generators of the 6th roots of unity are $$\frac{1}{2} \pm \frac{\sqrt{3}}{2}i$$. Is that correct?