Properties
Finite embedding problems characterize profinite groups. The following theorem gives an illustration for this principle.
Theorem. Let F be a countably (topologically) generated profinite group. Then
- F is projective if and only if any finite embedding problem for F is solvable.
- F is free of countable rank if and only if any finite embedding problem for F is properly solvable.
Read more about this topic: Embedding Problem
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