The Nonquadratic Imaginary Cyclic Fields of 2-power Degrees with Class Numbers Equal to Their Genus Class Numbers
نویسندگان
چکیده
It is known that there are only finitely many imaginary abelian number fields with class numbers equal to their genus class numbers. Here, we determine all the imaginary cyclic fields of 2-power degrees with class numbers equal to their genus class numbers.
منابع مشابه
Determination of All Nonquadratic Imaginary Cyclic Number Fields of 2-power Degrees with Ideal Class Groups of Exponents
We determine all nonquadratic imaginary cyclic number fields K of 2-power degrees with ideal class groups of exponents < 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 (Z/2Z)m , m > 0. There are 38 such number fields: 33 of them are quartic ones (see Theorem 13), 4 of them are octic ...
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