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This may be an obvious question, but in a mathematical context, what does "recover" mean? For example, one question on this website asked if it were possible to "recover a group from its homomorphisms," but I haven't been able to find a reference for what this means.

JeremyS
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    Think "reconstruct". – morrowmh Jan 16 '21 at 05:13
  • I think that in your specific case they are asking if the homomorphism uniquely determine (up to isomorphism) what the original group was. In other words, do the homomorphisms contain enough information to reconstruct the group. – Pedro Amaral Jan 16 '21 at 05:13
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    Infer, deduce, solve for, compute, .... – David G. Stork Jan 16 '21 at 05:14
  • It means to figure out what the group is (up to isomorphism). I think the phrasing is as if our knowledge of what the group is has been somehow lost, but we have this other information about the group at least, and we want to "recover" our knowledge of what the group is. But it's an idiomatic phrase and you shouldn't take the particular phrasing very seriously. – littleO Jan 16 '21 at 05:16

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