I have a homework problem I'm trying to do, but I'm not sure what it's asking. The problem is as follows:
Recall that $\mathbb{Q}/\mathbb{Z}$ is isomorphic to the group of all roots of unity in $\mathbb{C}$. Show that $\mathbb{Q}_p / \mathbb{Z}_p$ is isomorphic to the group of all $p$-power roots of unity. ($\mathbb{Z}_p$ is the p-adic integers, likewise $\mathbb{Q}_p$.)
What is the "group of all p-power roots of unity" in this context? Is it the union of the $p$-th roots of unity, $p^2$th roots of unity, $p^3$th roots of unity and so on? I don't think I've ever encountered the phrase before. (Presumably this is an obvious proof for some of you, and the answer is obvious, but for me I'm not so sure!)