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Published online by Cambridge University Press: 11 January 2016
We characterise number fields without a unit primitive element, and we exhibit some families of such fields with low degree. Also, we prove that a noncyclotomic totally complex number field $K$, with degree
$2d$ where
$d$ is odd, and having a unit primitive element, can be generated by a reciprocal integer if and only if
$K$ is not CM and the Galois group of the normal closure of
$K$ is contained in the hyperoctahedral group
$B_{d}$.