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

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...

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.

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 ( - 856 ) , we obtain Gal ( K u r / K ) ≅ S 4 ˜ × C 5 and K u r = K 4 , the fourth Hilbert class field of K . This is the first example of a number...