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Transactions of the American Mathematical Society

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On the construction of relative genus fields


Author: Gary Cornell
Journal: Trans. Amer. Math. Soc. 271 (1982), 501-511
MSC: Primary 12A65
MathSciNet review: 654847
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Abstract: We show how to construct the relative genus field in many cases. This is then applied to constructing fields with interesting class groups.


References [Enhancements On Off] (What's this?)

  • [1] A. Brumer, On the Picard group of $ {Q^{{\text{ab}}}}$ (to appear).
  • [2] G. Cornell, Relative genus theory and the class group of $ l$-extensions (in preparation).
  • [3] -, A note on the $ \hat Z$-extension of $ Q$ (in preparation).
  • [4] G. Frey, MR 50 #2126.
  • [5] A. Frölich, The genus field and genus group in finite number fields. I, II, Mathematika 6 (1959), 40–46, 142–146. MR 0113868
  • [6] -, The genus field and genus group in finite number fields. II, Mathematica 6 (1959), 142-146.
  • [7] Yoshiomi Furuta, The genus field and genus number in algebraic number fields, Nagoya Math. J. 29 (1967), 281–285. MR 0209260
  • [8] Makoto Ishida, The genus fields of algebraic number fields, Lecture Notes in Mathematics, Vol. 555, Springer-Verlag, Berlin-New York, 1976. MR 0435028
  • [9] Kenkichi Iwasawa, A note on class numbers of algebraic number fields, Abh. Math. Sem. Univ. Hamburg 20 (1956), 257–258. MR 0083013
  • [10] H. Kisilevsky, Some results related to Hilbert’s Theorem 94, J. Number Theory 2 (1970), 199–206. MR 0258793
  • [11] Serge Lang, Algebraic number theory, Addison-Wesley Publishing Co., Inc., Reading, Mass.-London-Don Mills, Ont., 1970. MR 0282947
  • [12] Lawrence C. Washington, Introduction to cyclotomic fields, Graduate Texts in Mathematics, vol. 83, Springer-Verlag, New York, 1982. MR 718674

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DOI: https://doi.org/10.1090/S0002-9947-1982-0654847-0
Article copyright: © Copyright 1982 American Mathematical Society