Let K/k$K/k$ be an extension of number fields and H_k$H_k$, H_K$H_K$ their respective Hilbert class fields. Is there a transfer map from Gal(H_k/k)$\text{Gal}(H_k/k)$ to Gal(H_K/K)$\text{Gal}(H_K/K)$?
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Glorfindel
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