Hello, I wonder which p-primary groups can be injected into a suitable direct sum of Prufer groups. I would suspect that ugly groups like the torsion part of $\prod \mathbb{Z}_{p^k}$ are not of this kind, but I was unable to figure it out. I would be grateful for any hint or reference.
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3$\begingroup$ Every abelian group can be embedded into its injective envelope, which is a $p$-group if the original group is. Then the envelope is a direct sum of Prüfer $p$-groups by the structure theorem for divisible groups. $\endgroup$– Emil JeřábekSep 16, 2012 at 13:45
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$\begingroup$ Thank you for a quick answer and apologies for not very MO question, I was being silly... $\endgroup$– Fred.FredSep 16, 2012 at 13:54
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