As I am currently writing up my [thesis][1] in English I noticed that I had referred to this result in the preface. It appears as Proposition 1 in an article by [Nakagoshi][2]. See also the recent article by [Cohen and Thorne](https://arxiv.org/abs/1609.09153 "On \$D_\ell\$-extensions of odd prime degree \$\ell\$").


  [1]: https://www.mathi.uni-heidelberg.de/~flemmermeyer/thesis.html "The construction of class fields"
  [2]: https://projecteuclid.org/journals/nagoya-mathematical-journal/volume-115/issue-none/On-the-unramified-extensions-of-the-prime-cyclotomic-number-field/nmj/1118781356.full "On the unramified extensions of the prime cyclotomic number field and its quadratic extensions"
  [3]: https://arxiv.org/pdf/1609.09153.pdf "On \$D_\ell\$-extensions of odd prime degree \$\ell\$"