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CM-Fields with Cyclic Ideal Class Groups of 2-Power Orders

✍ Scribed by Stéphane Louboutin

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
298 KB
Volume
67
Category
Article
ISSN
0022-314X

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✦ Synopsis

We prove that there are only finitely many CM-fields N with cyclic ideal class groups of 2-power orders such that the complex conjugation is the square of some automorphism of N. Since their actual determination would be too difficult, we only content ourselves with the determination of the nonquadratic imaginary cyclic number fields of 2-power degrees with cyclic ideal class groups of 2-power orders. There are exactly 22 such number fields, 10 of them having class number one, 9 of them having class number two, and 3 of them having class number four. This present determination is a nice complement to the determination of all nonquadratic imaginary cyclic number fields of 2-power degrees with ideal class groups of exponents 2 completed in an earlier paper.

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