On the n-torsion subgroup of the Brauer group of a number field
Journal de Théorie des Nombres de Bordeaux, Volume 15 (2003) no. 1, pp. 199-204.

Given a number field K Galois over the rational field ℚ, and a positive integer n prime to the class number of K, there exists an abelian extension L/K (of exponent n) such that the n-torsion subgroup of the Brauer group of K is equal to the relative Brauer group of L/K.

Pour toute extension galoisienne K de ℚ et tout entier positif n premier au nombre de classes de K, il existe une extension abélienne L de K d’exposant n telle que le n-sous-groupe de torsion du groupe de Brauer de K est égal au groupe de Brauer relatif de L/K.

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     title = {On the $n$-torsion subgroup of the {Brauer} group of a number field},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
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     publisher = {Universit\'e Bordeaux I},
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Hershy Kisilevsky; Jack Sonn. On the $n$-torsion subgroup of the Brauer group of a number field. Journal de Théorie des Nombres de Bordeaux, Volume 15 (2003) no. 1, pp. 199-204. doi : 10.5802/jtnb.397. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.397/

[1] E. Aljadeff, J. Sonn, Relative Brauer groups and m-torsion. Proc. Amer. Math. Soc. 130 (2002), 1333-1337. | MR | Zbl

[2] B. Fein, M. Schacher, Relative Brauer groups I. J. Reine Angew. Math. 321 (1981), 179-194. | MR | Zbl

[3] B. Fein, W. Kantor, M. Schacher, Relative Brauer groups II. J. Reine Angew. Math. 328 (1981), 39-57. | MR | Zbl

[4] B. Fein, M. Schacher, Relative Brauer groups III. J. Reine Angew. Math. 335 (1982), 37-39. | MR | Zbl

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