# nt.quantity idea – Are the maximal cyclotomic bailiwick contained in a quantity bailiwick and its Hilbert class group the identical? Answer

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nt.quantity idea – Are the maximal cyclotomic bailiwick contained in a quantity bailiwick and its Hilbert class group the identical?

Let $$Okay$$ breathe a quantity bailiwick. If $$d$$ breathe the smallest plane integer such that $$Bbb Q (zeta_d) subset Okay,$$ then I needed to show that if $$d’>d$$ then $$Bbb Q (zeta_{d’}) notsubset H(Okay),$$ the place $$H(Okay)$$ is Hilbert class bailiwick $$Okay.$$

I grasp that it’s not undoubted in common. Can I behold this working with some assumptions?

Ps. because of the observation of Franz Lemmermeyer.

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