Unramified quaternion extensions of quadratic number fields

Franz Lemmermeyer

Displaying similar documents to “Unramified quaternion extensions of quadratic number fields”

On determining the quadratic subfields of $Z_{2}$ -extensions of complex quadratic fields

Joseph E. Carroll (1975)

Compositio Mathematica

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Computations of Iwasawa invariants and $𝐊_{2}$

Alan Candiotti (1974)

Compositio Mathematica

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Maximal unramified extensions of imaginary quadratic number fields of small conductors

Ken Yamamura (1997)

Journal de théorie des nombres de Bordeaux

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We determine the structures of the Galois groups Gal $(K_{u r} / K)$ of the maximal unramified extensions $K_{u r}$ of imaginary quadratic number fields $K$ of conductors $≦ 420 (≦ 719$ under the Generalized Riemann Hypothesis). For all such $K$ , $K_{u r}$ is $K$ , the Hilbert class field of $K$ , the second Hilbert class field of $K$ , or the third Hilbert class field of $K$ . The use of Odlyzko’s discriminant bounds and information on the structure of class groups obtained by using the action of Galois groups on class groups is essential. We...

The class number one problem for the non-abelian normal CM-fields of degree 16

Stéphane Louboutin (1997)

Acta Arithmetica

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A quadratic field of prime discriminant requiring three generators for its class group, and related theory

Daniel Shanks, Peter Weinberger (1972)

Acta Arithmetica

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Quaternion Extensions of Order 16

Michailov, Ivo (2005)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: 12F12 We describe several types of Galois extensions having as Galois group the quaternion group Q16 of order 16. This work is partially supported by project of Shumen University.

Determination of all non-quadratic imaginary cyclic number fields of 2-power degree with relative class number ≤ 20

Young-Ho Park, Soun-Hi Kwon (1998)

Acta Arithmetica

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On normal radical extensions of real fields

David Gay (1979)

Acta Arithmetica

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Maximal unramified extensions of imaginary quadratic number fields of small conductors, II

Ken Yamamura (2001)

Journal de théorie des nombres de Bordeaux

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In the previous paper [15], we determined the structure of the Galois groups $Gal (K_{u r} / K)$ of the maximal unramified extensions $K_{u r}$ of imaginary quadratic number fields $K$ of conductors $≦ 1000$ under the Generalized Riemann Hypothesis (GRH) except for 23 fields (these are of conductors $≧ 723$ ) and give a table of $Gal (K_{u r} / K)$ . We update the table (under GRH). For 19 exceptional fields $K$ of them, we determine $Gal (K_{u r} / K)$ . In particular, for $K = 𝐐 (\sqrt{- 856})$ , we obtain $Gal (K_{u r} / K) ≅ \tilde{S_{4}} \times C_{5} and K_{u r} = K_{4}$ , the fourth Hilbert class field of $K$ . This is the first example of a number...

Initial layers of $Z_{l}$ -extensions of complex quadratic fields

J. E. Carroll, H. Kisilevsky (1976)

Compositio Mathematica

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