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}, mrnumber = {1360645}, zbl = {0826.11052}, language = {en}, url = {http://www.numdam.org/item/JTNB_1994__6_2_261_0/} }
TY - JOUR AU - Lemmermeyer, Franz TI - On $2$-class field towers of imaginary quadratic number fields JO - Journal de théorie des nombres de Bordeaux PY - 1994 SP - 261 EP - 272 VL - 6 IS - 2 PB - Université Bordeaux I UR - http://www.numdam.org/item/JTNB_1994__6_2_261_0/ LA - en ID - JTNB_1994__6_2_261_0 ER -
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/
[1] Number fields with 2-class groups isomorphic to (2, 2m), Austr. J. Math.
, ,[2] The groups of order 2n(n ≤ 6);, Macmillan, New York (1964). | Zbl
, ,[3] Zahlbericht, Physica Verlag, Würzburg, 1965.
,[4] Über die Klassenzahl abelscher Zahlkörper, Springer Verlag, Heidelberg. | Zbl
,[5] A note on the group of units of an algebraic number field, . Math. pures appl. 35 (1956), 189-192. | MR | Zbl
,[6] Sur le 2-groupe des classes d'idéaux des corps quadratiques, J. reine angew. Math. 283/284 (1974), 313-363. | EuDML | MR | Zbl
,[7] The Schur multiplier, London Math. Soc. monographs (1987), Oxford. | MR | Zbl
,[8] Number fields with class number congruent to 4 mod 8 and Hilbert's theorem 94, J. Number Theory 8 (1976), 271-279. | MR | Zbl
,[9] Über den 2-Klassenkörperturm eines quadratischen Zahlkörpers, J. reine angew. Math. 214/215 (1963), 201-206. | EuDML | MR | Zbl
,[10] Die Konstruktion von Klassenkörpern, Diss. Univ. Heidelberg (1994). | Zbl
,[11] Die Anzahl der durch 4 teilbaren Invarianten der Klassengruppe eines beliebigen quadratischen Zahlkörpers, J. reine angew. Math. 170 (1933), 69-74. | Zbl
, ,[12] Über die Lösbarkeit der Gleichung t2 - du2 = -4, Math. Z. 39 (1934), 95-111. | JFM | MR | Zbl
,[13] Abelsche Durchkreuzung, Monatsh. Math. Phys. 48 (1939), 340-352. | JFM | MR | Zbl
,