Displaying similar documents to “Dihedral extensions of Q of degree 21 which contain non-Galois extensions with class number not divisible by l”

The class number one problem for some non-abelian normal CM-fields of degree 24

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 𝒜 4 , the alternating group of degree 4 and order 12 . There are two such fields with Galois group 𝒜 4 × 𝒞 2 (see Theorem 14) and at most one with Galois group SL 2 ( 𝔽 3 ) (see Theorem 18); if the generalized Riemann hypothesis is true, then this last field has class number 1 .

On the Galois structure of the square root of the codifferent

D. Burns (1991)

Journal de théorie des nombres de Bordeaux

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Let L be a finite abelian extension of ℚ , with 𝒪 L the ring of algebraic integers of L . We investigate the Galois structure of the unique fractional 𝒪 L -ideal which (if it exists) is unimodular with respect to the trace form of L / ℚ .

Counting cyclic quartic extensions of a number field

Henri Cohen, Francisco Diaz y Diaz, Michel Olivier (2005)

Journal de Théorie des Nombres de Bordeaux

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In this paper, we give asymptotic formulas for the number of cyclic quartic extensions of a number field.