Chapter 7.3, Problem 11E

(a)

To determine

All elements of the subgroup $\langle a\rangle$, where $a=\cos \frac{2\pi }{3}+i\sin \frac{2\pi }{3}$ in $U_6$.

(b)

To determine

The order of $\langle a\rangle$, where $a=\cos \frac{2\pi }{3}+i\sin \frac{2\pi }{3}$ in $U_6$.

(c)

To determine

The generators of $\langle a\rangle$, where $a=\cos \frac{2\pi }{3}+i\sin \frac{2\pi }{3}$ in $U_6$.