Problem based on kronecker-weber theorem, Other Subject

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Problem based on kronecker-weber theorem

Question: Let K/Q be a finite Galois extension with abelian Galois group.

According to the Kronecker-Weber theorem: ∃m ∈ Z>0 such that: K ⊆ (ζm).

You have to prove: ∃f ∈ Z>0 such that for m:

K ⊆ Q(ζm) <==> f|m

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