## Subgroups of direct sum of a Prufer group

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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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. – Emil Jeřábek Sep 16 at 13:45
Thank you for a quick answer and apologies for not very MO question, I was being silly... – Fred.Fred Sep 16 at 13:54