All Questions

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 ...

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 ...