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

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.

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.

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     title = {On the $n$-torsion subgroup of the {Brauer} group of a number field},
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Kisilevsky, Hershy; Sonn, Jack. On the $n$-torsion subgroup of the Brauer group of a number field. Journal de théorie des nombres de Bordeaux, Tome 15 (2003) no. 1, pp. 199-204. http://www.numdam.org/item/JTNB_2003__15_1_199_0/

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