On $2$-class field towers of imaginary quadratic number fields

Lemmermeyer, Franz

Geodesic

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-class field towers of imaginary quadratic number fields

Lemmermeyer, Franz

Journal de théorie des nombres de Bordeaux, Tome 6 (1994) no. 2, pp. 261-272

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Résumé

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 $G = G a l (k^{2} / k)$ is abelian or metacyclic, and we will give $G$ in terms of generators and relations.

MR Zbl

@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},
     mrnumber = {1360645},
     zbl = {0826.11052},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JTNB_1994__6_2_261_0/}
}

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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://geodesic.mathdoc.fr/item/JTNB_1994__6_2_261_0/