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May 22, 2018 at 11:01 comment added YCor With some more efforts maybe one could get a countable example. We can replace the $p$-adics by rational $p$-adics, but then argument does not carry over when we use that $P^n/M$ is torsion... but it maybe possibly still holds that every decomposition has a finite summand.
May 22, 2018 at 10:58 comment added YCor Now fixed (after 5 years of intense thinking...)
May 22, 2018 at 10:18 history edited YCor CC BY-SA 4.0
fixed a few typos (changed $T$ to $L$ and prescribed $L\subset U$, which was implicit
Jun 29, 2013 at 18:55 comment added YCor you're right; I'll fix this if I need to edit something else.
Jun 29, 2013 at 17:53 vote accept Pete L. Clark
Jun 29, 2013 at 17:52 comment added Pete L. Clark Thanks very much. (This is very picky, but: I think you're not giving a counterexample but rather a negative answer to a question.)
Jun 29, 2013 at 15:30 history answered YCor CC BY-SA 3.0