Determination of all imaginary abelian sextic number fields with class number ≤ 11
Young-Ho Park, Soun-Hi Kwon (1997)
Acta Arithmetica
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Displaying similar documents to “The class number one problem for the non-normal sextic CM-fields. Part 2”
Determination of all imaginary abelian sextic number fields with class number ≤ 11
The class number one problem for some non-abelian normal CM-fields of degree
F. Lemmermeyer, S. Louboutin, R. Okazaki (1999)
Journal de théorie des nombres de Bordeaux
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We determine all the non-abelian normal CM-fields of degree 24 with class number one, provided that the Galois group of their maximal real subfields is isomorphic to , the alternating group of degree and order . There are two such fields with Galois group (see Theorem 14) and at most one with Galois group SL (see Theorem 18); if the generalized Riemann hypothesis is true, then this last field has class number .
The non-normal quartic CM-fields and the dihedral octic CM-fields with ideal class groups of exponent
Stéphane Louboutin, Hee-Sun Yang, Soun-Hi Kwon (2004)
Mathematica Slovaca
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Witt equivalence of quadratic extensions of global fields
Alfred Czogała (1991)
Mathematica Slovaca
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The imaginary cyclic sextic fields with class numbers equal to their genus class numbers
Stéphane Louboutin (1998)
Colloquium Mathematicae
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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 sextic fields with class numbers equal to their genus class numbers.
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 of the maximal unramified extensions of imaginary quadratic number fields of conductors under the Generalized Riemann Hypothesis (GRH) except for 23 fields (these are of conductors ) and give a table of . We update the table (under GRH). For 19 exceptional fields of them, we determine . In particular, for , we obtain , the fourth Hilbert class field of . This is the first example of a number...
The class number one problem for the dihedral and dicyclic CM-fields
Stéphane Louboutin (1999)
Colloquium Mathematicae
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We recall the determination of all the dihedral CM-fields with relative class number one, and prove that dicyclic CM-fields have relative class numbers greater than one.