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On Class Field Towers and the Rank of Ideal Class Groups
Published online by Cambridge University Press: 22 January 2016
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The following theorem on infinite class field towers is well-known.
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- Copyright © Editorial Board of Nagoya Mathematical Journal 1972
References
[1]
Brumer, A., Ramification and class towers of number fields, Michigan Math. J., 12 (1965), 129–131.CrossRefGoogle Scholar
[2]
Furuta, Y., The genus field and genus number in algebraic number fields, Nagoya Math. J., 29 (1967), 281–285.CrossRefGoogle Scholar
[3]
Furuta, Y., Über die zentrale Klassenzahl eines relativ-galoisschen Zahlkörpers, J. Number Theory, 3 (1971), 318–322.CrossRefGoogle Scholar
[4]
Golod, E. S. and Safarevic, y, On class field towers (Russian), Izv. Akad. Nauk SSSR, 28 (1964), 261–272 (Amer. Math. Soc. Transl., (2) 48, 91–102).Google Scholar
[5]
Iwasawa, K., A note on the group of units of an algebraic number field, J. Math. pures et appl., 35 (1956), 189–192.Google Scholar
[6]
Masuda, K., An application of the generalized norm residue symbol, Proc. Amer. Math. Soc., 10 (1959), 245–252.CrossRefGoogle Scholar
[7]
Šafareviě, I. R., Algebraic number fields (Russian), Proc. int. cong. Stockholm (1962), 163–176 (Amer. Math. Soc. Transl., (2) 31, 25–39).Google Scholar
[8]
Šafareviě, I. R., Extensions with given points of ramification (Russian), Publ. Math. I.H.E.S., 18 (1963), 71–95 (Amer. Math. Soc. Transl., (2) 59, 128–149).Google Scholar
[9]
Serre, J.-P., Cohomologie galoisienne, Lecture Notes in Math., 5 (1964), Springer-Verlag.Google Scholar
[10]
Serre, J.-P., Existence de tours infinies de corps de classes d’après Golod et Šafareviě, Le tendences géométrique en algebres et théorie de nombres, (1966), 231–238, Center national de la recherche Scientifique.Google Scholar
[11]
Roquette, P., On class field towers, Proc. instr. conf. at Brighton (Algebraic Number Theory), (1967), 231–249.Google Scholar
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