I am reading through Washington's book "Elliptic Curves Number Theory and cryptography" and I got stuck on the following line (see picture of text below).
"It is easy to see that $E[p^k]$ is cyclic".
I don't see why this is true. Perhaps it follows from the fact that since $E[p^k]$ contains an element of order $p^k$, the structure theorem for finite abelian groups implies that $E[p^k]\cong \mathbb{Z}/p^k\mathbb{Z}$, but I can't figure out the complete argument.
Any help is appreciated.
