# Is maximal cyclotomic bailiwick contained in quantity bailiwick and its hilbert classgroup identical? Answer

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Is maximal cyclotomic bailiwick contained in quantity bailiwick and its hilbert classgroup identical?

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

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