no. 2
On 2-class field towers of imaginary quadratic number fields
Journal de Théorie des Nombres de Bordeaux, Tome 6 (1994) no. 2, pp. 261-272.

For a number field k, let k 1 denote its Hilbert 2-class field, and put k 2 =(k 1 ) 1 . We will determine all imaginary quadratic number fields k such that G=Gal(k 2 /k) is abelian or metacyclic, and we will give G in terms of generators and relations.

@article{JTNB_1994__6_2_261_0,
     author = {Lemmermeyer, Franz},
     title = {On $2$-class field towers of imaginary quadratic number fields},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     pages = {261--272},
     publisher = {Universit\'e Bordeaux I},
     volume = {6},
     number = {2},
     year = {1994},
     zbl = {0826.11052},
     mrnumber = {1360645},
     language = {en},
     url = {www.numdam.org/item/JTNB_1994__6_2_261_0/}
}
Lemmermeyer, Franz. On $2$-class field towers of imaginary quadratic number fields. Journal de Théorie des Nombres de Bordeaux, Tome 6 (1994) no. 2, pp. 261-272. http://www.numdam.org/item/JTNB_1994__6_2_261_0/

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