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Determination of all nonquadratic imaginary cyclic number fields of $ 2$-power degrees with ideal class groups of exponents $ \leq 2$


Author: Stéphane Louboutin
Journal: Math. Comp. 64 (1995), 323-340
MSC: Primary 11R20; Secondary 11R29
DOI: https://doi.org/10.1090/S0025-5718-1995-1248972-6
MathSciNet review: 1248972
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Abstract: We determine all nonquadratic imaginary cyclic number fields K of 2-power degrees with ideal class groups of exponents $ \leq 2$, i.e., with ideal class groups such that the square of each ideal class is the principal class, i.e., such that the ideal class groups are isomorphic to some $ {({\mathbf{Z}}/2{\mathbf{Z}})^m},m \geq 0$. There are 38 such number fields: 33 of them are quartic ones (see Theorem 13), 4 of them are octic ones (see Theorem 12), and 1 of them has degree 16 (see Theorem 11).


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DOI: https://doi.org/10.1090/S0025-5718-1995-1248972-6
Article copyright: © Copyright 1995 American Mathematical Society