Kučera, Radan Different groups of circular units of a compositum of real quadratic fields. (English) Zbl 0807.11050 Acta Arith. 67, No. 2, 123-140 (1994). 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) Cited in 1 ReviewCited in 1 Document MSC: 11R27 Units and factorization 11R11 Quadratic extensions Keywords:abelian field; cyclotomic unit; real quadratic fields; circular units PDFBibTeX XMLCite \textit{R. Kučera}, Acta Arith. 67, No. 2, 123--140 (1994; Zbl 0807.11050) Full Text: DOI EuDML