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For a totally real (resp. imaginary) biquadratic number field $K$ with quadratic subfields $K_1$, $K_2$ and $K_3$, is there an explicit method to determine Hasse unit index $(U_K:U_{K_1}U_{K_2}U_{K_3})$?

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  • $\begingroup$ The Hasse unit index of $L/K$ is $[\mathcal{O}_L^\times :\mathcal{O}_{L,torsion}^\times \mathcal{O}_{K}^\times]$ ? $\endgroup$ – reuns Jun 20 '17 at 10:21
  • $\begingroup$ Are you looking for the Brauer-Kuroda formula like in Proposition (4.1) in de Smit's article www.math.leidenuniv.nl/~desmit/prep/braukur.ps ? $\endgroup$ – Chris Wuthrich Jun 20 '17 at 13:01
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    $\begingroup$ H. Wada, On the class number and the unit group of certain algebraic number fields, J. Fac. Sci. Univ. Tokyo 13 (1966), 201–209 $\endgroup$ – Franz Lemmermeyer Jun 21 '17 at 14:10

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