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The class number of pure fields of prime degree

Published online by Cambridge University Press:  26 February 2010

Charles J. Parry  and
Colin D. Walter
Charles J. Parry
Affiliation:
Department of Mathematics, VPI & SU, Blacksburg, Virginia, U.S.A.
Colin D. Walter
Affiliation:
Department of Mathematics, University College, Dublin
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Extract

Here we give necessary and sufficient conditions foi a prime ι to divide the class number of the Galois closure of a pure field of degree ι over the rationals. The work extends that of Honda in [4] and that of the first author in [8].

Type
Research Article
Information
Mathematika , Volume 23 , Issue 2 , December 1976 , pp. 220 - 226
Copyright
Copyright © University College London 1976

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References

1.Ayoub, R.. An introduction to the analytic theory of numbers (Amer. Math. Soc., Providence, R.I., 1963).Google Scholar
2.Borevich, Z. I. and Shafarevich, I. R.. Number theory (Academic Press, New York, 1966).Google Scholar
3.Hasse, H.. Bericht über Neuere Untersuchungen und Probleme aus der Theorie der algebraischen Zahlkörper (Physcia-Verlag, Würzburg/Wien, 1970).Google Scholar
4.Honda, T.. “Pure cubic fields whose class numbers are multiples of three”, J. of Number Theory, 3 (1971), 7–12.CrossRefGoogle Scholar
5.Iwasawa, K.. “A note on class numbers of algebraic number fields”, Abh. Math. Sent. UnivHamburg, 20 (1956), 257–258.CrossRefGoogle Scholar
6.Janusz, G. J.. Janusz. Algebraic number fields (Academic Press, New York, 1973).Google Scholar
7.Moriya, M.. “Über die Klassenzahl eines relativ-zyklischen Zahlkörpers vom Primzahlgrad”, Proc. Imper. Acad. Japan, 6 (1930), 245–247.Google Scholar
8.Parry, C.. “Class number relations in pure quintic fields”, Symposia Mathematica, 15 (1975), 475–485.Google Scholar
9.Van der Waall, R.. “On the conductor of the non-abelian simple character of the galois group of a special field extension”, Symposia Mathematica, 15 (1975), 389–395.Google Scholar