I have read that for any prime number $p$ the Prüfer $p$-group is countable.
My question is: where can I find a proof of this fact?
Thanks.
I have read that for any prime number $p$ the Prüfer $p$-group is countable.
My question is: where can I find a proof of this fact?
Thanks.
It is can be viewed as a subset of the group $\mathbb{Q}/\mathbb{Z}$, which is obviously countable.
The subset representing the Prüfer group is just the set of all elements with order a power of $p$.