For some algebraic number fields $F$ with only one fundamental unit, we give a lower bound of the extension degree of the ray class field of conductor a rational prime $p$ over the Hilbert class field of $F$.
"Distribution of units of algebraic number fields with only one fundamental unit." Proc. Japan Acad. Ser. A Math. Sci. 80 (6) 86 - 89, June 2004. https://doi.org/10.3792/pjaa.80.86