On ideal class groups of 2-power exponent

Earnest, A. G.; Körner, O. H.

doi:10.1090/S0002-9939-1982-0667271-7

On ideal class groups of $2$-power exponent
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by A. G. Earnest and O. H. Körner PDF

Proc. Amer. Math. Soc. 86 (1982), 196-198 Request permission

Abstract:

It is shown that for a fixed totally real algebraic number field $k$ and a fixed positive integer $t$, there exist only finitely many totally imaginary quadratic extensions $K$ of $k$ having ideal class groups of exponent ${2^t}$.

References

David W. Boyd and H. Kisilevsky, On the exponent of the ideal class groups of complex quadratic fields, Proc. Amer. Math. Soc. 31 (1972), 433–436. MR 289454, DOI 10.1090/S0002-9939-1972-0289454-4

An extension of Heilbronn’s class number theorem

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A. G. Earnest and Dennis R. Estes, An algebraic approach to the growth of class numbers of binary quadratic lattices, Mathematika 28 (1981), no. 2, 160–168 (1982). MR 645096, DOI 10.1112/S0025579300010214

Bericht über neuere Untersuchungen und Probleme aus der Theorie der algebraischen Zahlkörpern

H. M. Stark, Some effective cases of the Brauer-Siegel theorem, Invent. Math. 23 (1974), 135–152. MR 342472, DOI 10.1007/BF01405166
P. J. Weinberger, Exponents of the class groups of complex quadratic fields, Acta Arith. 22 (1973), 117–124. MR 313221, DOI 10.4064/aa-22-2-117-124