Determination of all nonquadratic imaginary cyclic number fields of $2$-power degrees with ideal class groups of exponents $\leq 2$
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- by Stéphane Louboutin PDF
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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).References
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Additional Information
- © Copyright 1995 American Mathematical Society
- 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