In this paper, we determine the first Hilbert $2$-class field for some quartic cyclic number fields ${\mathrm k}$ and the Galois group of the second Hilbert $2$-class field of ${\mathrm k}$ over ${\mathrm k}$.
@article{27471, title = {Sur la tour de Hilbert de certains corps}, journal = {Boletim da Sociedade Paranaense de Matem\'atica}, volume = {34}, year = {2015}, doi = {10.5269/bspm.v34i2.27471}, language = {FR}, url = {http://dml.mathdoc.fr/item/27471} }
Azizi, Abdelmalek; Talbi, Mohammed; Talbi, Mohamed. Sur la tour de Hilbert de certains corps. Boletim da Sociedade Paranaense de Matemática, Tome 34 (2015) . doi : 10.5269/bspm.v34i2.27471. http://gdmltest.u-ga.fr/item/27471/