Given a regular n-gon. Let r be rotation of it by $\frac{2\pi}{n}$ radians. Then $C_n$ = {$e,r,r^2,...,r^{n-1}$}
I have to find all minimal generating sets of $C_6$. I see that r is needed for minimal set. But book says it has minimal sets of two elements also. I am thinking about horizontal translation in upper and lower side of hexagon but not sure
One of the generating sets can be $\{r\}$ alone. Another one could be $\{r^{2},r^{3}\}$ i.e., take two elements such that one does not lie in the subgroup generated by another, then the set containing these two elements can act as generating set. Making Cayley digraphs can help a lot in such cases.