Remark on the divisibility of the class numbers of certain quartic number fields by 5

Endô, Akira

doi:10.1090/S0002-9939-1984-0746079-X

Remark on the divisibility of the class numbers of certain quartic number fields by $5$
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by Akira Endô

Proc. Amer. Math. Soc. 91 (1984), 513-517

DOI: https://doi.org/10.1090/S0002-9939-1984-0746079-X

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Abstract:

The congruence relation modulo 5 between the class numbers of the real and imaginary quartic subfields of the extension of a quadratic number field obtained by adjoining a fifth root of unity is studied.

References

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Über die Klassenzahlen algebraischer Zahlkörper

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Charles J. Parry, On the class number of relative quadratic fields, Math. Comp. 32 (1978), no. 144, 1261–1270. MR 502013, DOI 10.1090/S0025-5718-1978-0502013-4