Abstract
This paper studies infinite class field towers of number fields K that are ramified over \({\mathbb{Q}}\) only at one finite prime. In particular, we show the existence of such towers for a general family of primes including p = 2, 3 and 5.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Daberkow M. (2001). On computations in Kummer extensions. J. Symb. Comput. 31: 113–131
Golod, E., Šhafarevič, I.: On class field towers. Izv. Akad. Nauk SSSR, 28, 261–272 (1964) (Russian); English translation: Am. Math. Soc. Trans. 48, 91–102 (1965)
Hajir, F.: On a theorem of Koch. Pac. J. Math., 176(1), 15–18 (1996). [See also, Correction to: “On a theorem of Koch”, Pac. J. Math., 196(2), 507–508 (2000)]
Koch H. and Venkov B.B. (1975). Über den p-Klassenkörperturm eines imaginär quadratischen Zahlkörpers. Astérisque 24/25: 57–67
Schoof R. (1986). Infinite class field towers of quadratic fields. Journal fur die reine und angewandte Mathematik 372: 209–220
Schmithals B. (1980). Konstruktion imaginärquadratischer Körper mit unendlichem Klassenkörperturm. Archiv. Math. 34: 307–312
Shatz S.S. (1972). Profinite groups, arithmetic and geometry, Annals of Mathematics Studies (67). Princeton University Press, Princeton
The PARI-Group, PARI/GP, Version 2.3.1, Bordeaux, (2006), available from http://pari.math.u-bordeaux.fr/
Washington L.C. (1996). Introduction to Cyclotomic Fields, Graduate Texts in Mathematics. Springer, Berlin
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Hoelscher, J.L. Infinite class field towers. Math. Ann. 344, 923–928 (2009). https://doi.org/10.1007/s00208-009-0334-8
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00208-009-0334-8