"Introduction to Commutative Algebra" by Atiyah-Macdonald says the following:
Let $G_n$ be the subgroup containing elements of order $p^n$ in the group $\Bbb{Q/Z}$ for all $n\in\Bbb{N}$. Here $p$ is a prime number. Then $G_1\subset G_2\subset G_3\subset\dots$
I can understand that $G_1$ would be such a subgroup. But how would $G_2$ be a subgroup where every element is of order $p^2$? The elements in $G_2$ would be $\overline{0},\overline{1/p^2},\overline{2/p^2},\dots$ Then $\overline{p/p^2}$ would be of order $p$, and not $p^2$!
Where am I going wrong?