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Jan 5, 2012 at 20:56 comment added Jonathan Kiehlmann Very good question. The easiest response is "something very big". It is $\aleph_{1}$-based and has a direct summand isomorphic to $\prod_{\aleph_{0}}\mathbb{Z}_{p}$. (The latter as $\prod_{i\in\mathbb{N}} C_{p^{i}}$ has a direct summand isomorphic to $\prod_{\aleph_{0}}\mathbb{Z}_{p}$.) Not sure of an exact answer, but will think more of it. Feel free to e-mail me with any more questions.
Jan 5, 2012 at 13:54 comment added candl out of curiousity, what exactly is the profinite completion of $\prod_i C_{p^i}$
Nov 30, 2011 at 3:20 history edited Jonathan Kiehlmann CC BY-SA 3.0
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Nov 30, 2011 at 1:57 history answered Jonathan Kiehlmann CC BY-SA 3.0