All Questions

Let $\mathit{Profinite}_{\mathrm{Ab}}$ be the category of profinite abelian groups, and let $\mathit{Profinite}_{\mathrm{Set}}$ be the category of profinite sets. Does the forgetful functor $$\mathit{...

It is well known that every subgroup $H$ of a finite abelian group $G$ is isomorphic to a quotient of $G$. I'm wondering whether there is a counterpart for profinite groups. For example is it true ...

Does anyone know of any interesting examples of an infinite abelian $p$-group which is uncountable? By non-interesting here I mean the direct sums of cylic and quasi-cylic groups, and totally ...