For a number field , let denote its Hilbert -class field, and put . We will determine all imaginary quadratic number fields such that is abelian or metacyclic, and we will give 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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