## Galois module structure of units in real biquadratic number fields.(English)Zbl 1060.11070

Let $$p$$ and $$q$$ be primes and consider the bicyclic number field $$N = \mathbb Q(\sqrt{p},\sqrt{q}\,)$$. If the quadratic subfield $$K = \mathbb Q(\sqrt{pq}\,)$$ has elementary abelian $$2$$-class group, then the structure of the unit group of $$N$$ can easily be described in terms of the fundamental units of the quadratic subfields of $$N$$. In the case where the class number $$h(K)$$ is divisible by $$4$$, the authors construct the corresponding governing field for divisibility by $$8$$ [cf. P. Stevenhagen’s thesis, Publ. Math. Fac. Sci. Besançon, Théor. Nombres 1988/89, No. 1, 93 p. (1989; Zbl 0701.11056)] and give the structure of the unit group of $$N$$ for those fields for which $$h(K)$$ is not divisible by $$8$$.
In a second part, the authors study the existence of Minkowski units in general bicyclic biquadratic number fields.

### MSC:

 11R16 Cubic and quartic extensions 11R29 Class numbers, class groups, discriminants

Zbl 0701.11056
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