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

Louboutin, Stéphane

doi:10.1090/S0025-5718-1995-1248972-6

Determination of all nonquadratic imaginary cyclic number fields of $2$-power degrees with ideal class groups of exponents $\leq 2$
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Math. Comp. 64 (1995), 323-340 Request permission

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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