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Hasse unit indices of dihedral octic CM-fields. (English) Zbl 0972.11105
By modifying ideas of T. Kubota [Nagoya Math. J. 10, 65–85 (1956; Zbl 0074.03001)] for computing square roots of units in bicyclic quartic extensions of the rationals, the author develops a method for calculating the Hasse unit index $$(E_N : W_NE^+)$$ of octic dihedral CM-fields $$N$$; here $$E_N$$ is the unit group of $$N$$, $$E^+$$ is the unit group of the maximal real subfield of $$N$$, and $$W_N$$ is the group of roots of unity contained in $$N$$. The method is illustrated by an example.

##### MSC:
 11R27 Units and factorization 11R21 Other number fields
##### Keywords:
unit group; Hasse unit index; dihedral extension; CM fields
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##### References:
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