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ON NUMBER FIELDS WITHOUT A UNIT PRIMITIVE ELEMENT
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 93 / Issue 3 / June 2016
- Published online by Cambridge University Press:
- 11 January 2016, pp. 420-432
- Print publication:
- June 2016
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- Article
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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 
$B_{d}$.
