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**hmmmm** Let G be a finite group of rotations of the plane around the origin, prove that G is cyclic.

Im confused about how to start this (I have not done any group theory in a while)

Thanks for any help

Take the smallest rotation, denoted as g, then there exists a least m such that $\displaystyle g^m=1$

If m=n then we are done. $\displaystyle \{1,g,g^2,.....,g^{m-1}\}$

what is n??

If $\displaystyle m<n$

then there exists an element $\displaystyle b\in G$ s.t. $\displaystyle b\neq g^i$

do I then go on to show that if this was the case b must have an inverse and that would be one of the $\displaystyle g^i's$ the we have a contradiction?