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Different groups of circular units of a compositum of real quadratic fields. (English) Zbl 0807.11050

There are many different definitions of the group of circular (or cyclotomic) units of a real abelian field in the literature. The paper compares groups given by the definitions of Hasse, Leopoldt, Gras, Gillard, Sinnott and Washington for the special case of abelian fields, namely for a compositum \(k\) of (any finite number of) real quadratic fields such that \(-1\) is not a square in the genus field \(K\) of \(k\) in the narrow sense.
The reason why the fields of this type are considered is as follows. In the field of this type we can define a group \(C\) of units (slightly bigger than Sinnott’s group of circular units) such that the Galois group acts on \(C/ (\pm C^ 2)\) trivially, which allows an explicit construction of independent generators of \(C\). In the paper these generators are used for finding independent generators of the other groups of units and computing their relative indices.
Reviewer: R.Kučera (Brno)

MSC:

11R27 Units and factorization
11R11 Quadratic extensions
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